You are absolutely right to say that the translator of the the Pentateuch was rather conservative in his translation, often when it differs it can be found to be following a text similar to the Samaritan Pentateuch. In this instance the translator saw the same word that we have in the MT. Moreover I do not think this is an attempt to obscure the problem of Isaac being one of two sons. I think it is more likely that the Genesis translator encountered a word he was unfamiliar with. In other instances where the translator encounters rare words he reads the context and makes his best guess at defining the word contextually.
Probably the most obvious and influential instances of this is in Genesis 1:2 where He encountered חהו ובהו which the American Standard Version accurately translated as "waste and void" (G's influence survives today in the word "unformed"). Not knowing what these very rare words meant He determined that the earth was αορατος και ακατασκευστος or unseen and unfurnished, descriptions which he arrived at due to the fact that the earth was covered with darkness, dry ground had not appeared, and all the hosts(creatures) had not been created. This method of filling his knowledge gap skirts around rare words but creates the unfortunate side-effect of being redundant.
I think this is the case here too. The word יחיד is relatively rare, only occurring 12 times in the MT. It is defined in Holladay's Concise HALOT as "1. only; 2. lonely, abandoned". Ultimately יחיד was translated three ways into Greek: Genesis, Proverbs, Jeremiah, Amos and Zechariah all translate it with αγαπη- forms. Psalms translates it twice as μονογενη, once μονοτρόπους. Judges translates it in both ways! Of the words 12 biblical occurrences 8 times it is translated "beloved". "Beloved" became the standard translation (a calque) of יחיד used by the various Septuagint Translators. I think that this technique is a rather honest way for him to handle his linguistic limitations, much more preferable than omitting the word or taking "wild guesses", he still maintains his interlinear word-for-word style. I would not describe this as taking liberty.
Genesis 22:2
וַיֹּאמֶר קַח־נָא אֶת־בִּנְךָ אֶת־יְחִידְךָ אֲשֶׁר־אָהַבְתָּ
אֶת־יִצְחָק וְלֶךְ־לְךָ אֶל־אֶרֶץ הַמֹּרִיָּה וְהַעֲלֵהוּ שָׁם לְעֹלָה
עַל אַחַד הֶהָרִים אֲשֶׁר אֹמַר אֵלֶיךָ׃ (WLC)
He said, “Take your son, your only son Isaac, whom you love, and go to
the land of Moriah, and offer him there as a burnt offering on one of
the mountains that I shall show you.” (NRSV)
καὶ εἶπεν Λαβὲ τὸν υἱόν σου τὸν ἀγαπητόν, ὃν ἠγάπησας, τὸν Ισαακ, καὶ
πορεύθητι εἰς τὴν γῆν τὴν ὑψηλὴν καὶ ἀνένεγκον αὐτὸν ἐκεῖ εἰς
ὁλοκάρπωσιν ἐφ᾽ ἓν τῶν ὀρέων, ὧν ἄν σοι εἴπω. (Rahlfs-Hanhart)
And he said, “Take your beloved son Isaak, whom you love, and go into
the high land, and offer him as a whole burnt offering on one of the
mountains, whichever I mention to you.” (NETS)
CCATS Variants show Sev 467 Arab (2nd) read μονογενη, LaK(Cyprian) reads unicum, and SyhB(unedited lectionary readings by Baars) read + unicum. Aquilas reads τον μονογενη Symmachus τον μονον. 343 reads a conflation τον μονογενη τον αγαπητον. We do not have the extant readings from Theodotian.
The reading μονογενη likely existed in translation in the first century due to its use in the Epistle to the Hebrews 11:17 (Πίστει προσενήνοχεν Ἀβραὰμ τὸν Ἰσαὰκ πειραζόμενος καὶ τὸν μονογενῆ προσέφερεν, ὁ τὰς ἐπαγγελίας ἀναδεξάμενος,) It would not surprise me if this (τὸν μονογενῆ) was under the influence of Theodotian.
Genesis 22:12
וַיֹּאמֶר אַל־תִּשְׁלַח יָדְךָ אֶל־הַנַּעַר וְאַל־תַּעַשׂ לוֹ
מְאוּמָּה כִּי עַתָּה יָדַעְתִּי כִּי־יְרֵא אֱלֹהִים אַתָּה וְלֹא
חָשַׂכְתָּ אֶת־בִּנְךָ אֶת־יְחִידְךָ מִמֶּנִּי׃ (WLC)
καὶ εἶπεν Μὴ ἐπιβάλῃς τὴν χεῖρά σου ἐπὶ τὸ παιδάριον μηδὲ ποιήσῃς αὐτῷ
μηδέν· νῦν γὰρ ἔγνων ὅτι φοβῇ τὸν θεὸν σὺ καὶ οὐκ ἐφείσω τοῦ υἱοῦ σου
τοῦ ἀγαπητοῦ δι᾽ ἐμέ. (Rahlfs-Hanhart)
He said, “Do not lay your hand on the boy or do anything to him; for
now I know that you fear God, since you have not withheld your son,
your only son, from me.” (NRSV)
And he said, “Do not lay your hand on the youngster nor do anything to
him. For now I know that you do fear God, and for my sake you have not
spared your beloved son.” (NETS)
**There is no textual-critical issue in the Greek according to CCATS Variants.
Genesis 22:16
וַיֹּאמֶר בִּי נִשְׁבַּעְתִּי נְאֻם־יְהוָה כִּי יַעַן אֲשֶׁר עָשִׂיתָ
אֶת־הַדָּבָר הַזֶּה וְלֹא חָשַׂכְתָּ אֶת־בִּנְךָ אֶת־יְחִידֶךָ׃ (WLC)
λέγων Κατ᾽ ἐμαυτοῦ ὤμοσα, λέγει κύριος, οὗ εἵνεκεν ἐποίησας τὸ ῥῆμα
τοῦτο καὶ οὐκ ἐφείσω τοῦ υἱοῦ σου τοῦ ἀγαπητοῦ δι᾽ ἐμέ, (Rahlfs-Hanhart)
and said, “By myself I have sworn, says the Lord: Because you have
done this, and have not withheld your son, your only son, (NRSV)
saying, “By myself I have sworn, says the Lord: Inasmuch as you have
carried out this matter and for my sake have not spared your beloved
son, (NETS)
**There is no textual-critical issue in the Greek according to CCATS Variants.
Judges 11:34
וַיָּבֹא יִפְתָּח הַמִּצְפָּה אֶל־בֵּיתוֹ וְהִנֵּה בִתּוֹ יֹצֵאת
לִקְרָאתוֹ בְתֻפִּים וּבִמְחֹלוֹת וְרַק הִיא יְחִידָה אֵין־לוֹ
מִמֶּנּוּ בֵּן אוֹ־בַת׃ (WLC)
Καὶ ἦλθεν Ιεφθαε εἰς Μασσηφα εἰς τὸν οἶκον αὐτοῦ, καὶ ἰδοὺ ἡ θυγάτηρ
αὐτοῦ ἐξεπορεύετο εἰς ἀπάντησιν αὐτοῦ ἐν τυμπάνοις καὶ χοροῖς· καὶ
αὕτη μονογενὴς αὐτῷ ἀγαπητή, καὶ οὐκ ἔστιν αὐτῷ πλὴν αὐτῆς υἱὸς ἢ
θυγάτηρ. (Rahlfs-Hanhart)
Then Jephthah came to his home at Mizpah; and there was his daughter
coming out to meet him with timbrels and with dancing. She was his
only child; he had no son or daughter except her. (NRSV)
And Iephthae came to Massepha, to his home, and see, his daughter was
coming out to meet him with timbrels and with dancing. And she was his
beloved only child, and he had no son or daughter except her. (NETS)
It should be noted here, that הִיא יְחִידָה receives a double translation as αὕτη μονογενὴς αὐτῷ ἀγαπητή, although some might be tempted to say that the LXX Vorlage was different from the MT; it is more likely that the difference is due to the inclusion of αγαπητη due to its status as a calque for יחיד.
A Gottingen or CCATS apparatus does not exist. So the text here is a little uncertain. Some texts omit αὐτῷ ἀγαπητή (Manuscripts BNq). Many of the miniscules also include περιψυκτος (Manuscripts dglnoptvw) *See Cambridge Large Septuagint.
Psalm E22:20 H22:21 G21:21
הַצִּילָה מֵחֶרֶב נַפְשִׁי מִיַּד־כֶּלֶב יְחִידָתִי׃ (WLC)
ῥῦσαι ἀπὸ ῥομφαίας τὴν ψυχήν μου
καὶ ἐκ χειρὸς κυνὸς τὴν μονογενῆ
μου· (Rahlfs-Hanhart)
Deliver my soul from the sword,
my life from the power of the dog!
(NRSV)
Rescue my soul from the sword,
and from a dog’s claw my only life!
(NETS)
Deliver my soul from the sword;
my darling from the power of the
dog. (KJV)
Deliver my soul from the sword;
Mine only one from the power of the
dog. (JPS)
As can be seen there in both the MT and LXX there is no word for life in the second line. This is obscured by the NETS policy of following NRSV. JPS is the most accurate, and it is possible that even KJV is possible if we consider that μονογενη and יחיד could have adopted a colloquial value something like "special" or "favorite".
Psalm 25:16/ G24:16
פְּנֵה־אֵלַי וְחָנֵּנִי
כִּי־יָחִיד וְעָנִי אָנִי׃ (WLC)
ἐπίβλεψον ἐπ᾽ ἐμὲ καὶ ἐλέησόν με,
ὅτι μονογενὴς καὶ πτωχός εἰμι
ἐγώ. (Rahlfs-Hanhart)
Turn to me and be gracious to me, for I am lonely and afflicted.
(NRSV)
Look upon me and have mercy on me, because I am an only child and
poor. (NETS)
Psalm 35:17/ G34:17
אֲדֹנָי כַּמָּה תִּרְאֶה הָשִׁיבָה נַפְשִׁי מִשֹּׁאֵיהֶם מִכְּפִירִים
יְחִידָתִי׃ אֲדֹנָי כַּמָּה תִּרְאֶה הָשִׁיבָה נַפְשִׁי מִשֹּׁאֵיהֶם
מִכְּפִירִים יְחִידָתִי׃ (WLC)
κύριε, πότε ἐπόψῃ;
ἀποκατάστησον τὴν ψυχήν μου ἀπὸ τῆς κακουργίας
αὐτῶν,
ἀπὸ λεόντων τὴν μονογενῆ μου. (Rahlfs-Hanhart)
How long, O Lord, will you look on?
Rescue me from their ravages,
my life from the lions! (NRSV)
O Lord, when will you take a look?
Restore my soul from their
ravages,
from lions my only one! (NETS)
Psalm E68:6 H68:7 G67:7
אֱלֹהִים מוֹשִׁיב יְחִידִים בַּיְתָה מוֹצִיא אֲסִירִים בַּכּוֹשָׁרוֹת
אַךְ סוֹרֲרִים שָׁכְנוּ צְחִיחָה׃ (WLC)
ὁ θεὸς κατοικίζει μονοτρόπους ἐν οἴκῳ
ἐξάγων πεπεδημένους ἐν
ἀνδρείᾳ,
ὁμοίως τοὺς παραπικραίνοντας τοὺς κατοικοῦντας ἐν
τάφοις. (Rahlfs-Hanhart)
God setteth the solitary in families:
He bringeth out the
prisoners into prosperity;
But the rebellious dwell in a parched
land. (NRSV)
God settles solitary ones into a home,
leading out prisoners with
manliness,
likewise those who embitter them that live in tombs.
(NETS)
This is the only time יחיד is plural and the LXX did a good job not calquing it.
Proverbs 4:3
כִּי־בֵן הָיִיתִי לְאָבִי רַךְ
וְיָחִיד לִפְנֵי אִמִּי׃ (WLC)
υἱὸς γὰρ ἐγενόμην κἀγὼ πατρὶ ὑπήκοος
καὶ ἀγαπώμενος ἐν προσώπῳ
μητρός, (Rahlfs-Hanhart)
When I was a son with my father,
tender, and my mother’s
favorite, (NRSV)
For I became a son, and I am obedient to my father
and beloved in
the eyes of my mother, (NETS)
Ta-dah NRSV is saying that יחיד can mean favorite!
So after seeing all that its not too surprising to find that Jeremiah, Amos, and Zechariah are all translated using this calque.
Jeremiah 6:26
בַּת־עַמִּי חִגְרִי־שָׂק וְהִתְפַּלְּשִׁי בָאֵפֶר אֵבֶל יָחִיד עֲשִׂי
לָךְ מִסְפַּד תַּמְרוּרִים כִּי פִתְאֹם יָבֹא הַשֹּׁדֵד עָלֵינוּ׃
(WLC)
θύγατερ λαοῦ μου, περίζωσαι σάκκον,
κατάπασαι ἐν σποδῷ,
πένθος
ἀγαπητοῦ ποίησαι σεαυτῇ,
κοπετὸν οἰκτρόν,
ὅτι ἐξαίφνης ἥξει
ταλαιπωρία ἐφ᾽ ὑμᾶς. (Rahlfs-Hanhart)
my poor people, put on sackcloth,
and roll in ashes;
make
mourning as for an only child,
most bitter lamentation:
for
suddenly the destroyer will come upon us. (NRSV)
O daughter of my people, put on sackcloth;
sprinkle with ashes;
make for yourself a mourning for a beloved,
a most pitiable
lamentation:
because suddenly distress will come upon us. (NETS)
Amos 8:10
וְהָפַכְתִּי חַגֵּיכֶם לְאֵבֶל וְכָל־שִׁירֵיכֶם לְקִינָה וְהַעֲלֵיתִי
עַל־כָּל־מָתְנַיִם שָׂק וְעַל־כָּל־רֹאשׁ קָרְחָה וְשַׂמְתִּיהָ
כְּאֵבֶל יָחִיד וְאַחֲרִיתָהּ כְּיוֹם מָר׃ (WLC)
καὶ μεταστρέψω τὰς ἑορτὰς ὑμῶν εἰς πένθος
καὶ πάσας τὰς ᾠδὰς ὑμῶν
εἰς θρῆνον
καὶ ἀναβιβῶ ἐπὶ πᾶσαν ὀσφὺν σάκκον
καὶ ἐπὶ πᾶσαν
κεφαλὴν φαλάκρωμα
καὶ θήσομαι αὐτὸν ὡς πένθος ἀγαπητοῦ
καὶ τοὺς
μετ᾽ αὐτοῦ ὡς ἡμέραν ὀδύνης. (Rahlfs-Hanhart)
I will turn your feasts into mourning,
and all your songs into
lamentation;
I will bring sackcloth on all loins,
and baldness on
every head;
I will make it like the mourning for an only son,
and
the end of it like a bitter day. (NRSV)
And I will turn your feasts into mourning
and all your songs into
lamentation.
And I will bring sackcloth on every loin
and
baldness on every head.
And I will make him like the mourning for a
loved one
and those with himb like a day of suffering. (NETS)
Zechariah 12:10
שָׁפַכְתִּי עַל־בֵּית דָּוִיד וְעַל יוֹשֵׁב יְרוּשָׁלִַם רוּחַ חֵן
וְתַחֲנוּנִים וְהִבִּיטוּ אֵלַי אֵת אֲשֶׁר־דָּקָרוּ וְסָפְדוּ עָלָיו
כְּמִסְפֵּד עַל־הַיָּחִיד וְהָמֵר עָלָיו כְּהָמֵר עַל־הַבְּכוֹר׃ (WLC)
καὶ ἐκχεῶ ἐπὶ τὸν οἶκον Δαυιδ καὶ ἐπὶ τοὺς κατοικοῦντας Ιερουσαλημ
πνεῦμα χάριτος καὶ οἰκτιρμοῦ, καὶ ἐπιβλέψονται πρός με ἀνθ᾽ ὧν
κατωρχήσαντο καὶ κόψονται ἐπ᾽ αὐτὸν κοπετὸν ὡς ἐπ᾽ ἀγαπητὸν καὶ
ὀδυνηθήσονται ὀδύνην ὡς ἐπὶ πρωτοτόκῳ. (Rahlfs-Hanhart)
And I will pour out a spirit of compassion and supplication on the
house of David and the inhabitants of Jerusalem, so that, when they
look on the one whom they have pierced, they shall mourn for him, as
one mourns for an only child, and weep bitterly over him, as one weeps
over a firstborn. (NRSV)
And I will pour out a spirit of grace and compassion on the house of
Dauid and on the inhabitants of Ierousalem, and they shall look to me
because they have danced triumphantly, and they shall mourn for him
with a mourning as for a loved one, and they shall be pained with pain
as for a firstborn. (NETS)
WELL THATS IT! All Twelve Instances of יחיד.