I, along with scholars everywhere, deeply respect the work of BDAG. I have no quibble with his observation of the change in the colloquial usage to the the gradual use of μέλλω with the infinitive as a simple future. However, I don't think it an expected categorization to lump Luke-Acts in with colloquial Koine authors. By all accounts, he's rather erudite and sophisticated in his command and use of Greek. So while I don't think Luke is above such a usage, I think it inappropriate to presume it:
① to take place at a future point of time and so to be subsequent to
another event, be about to, used w. an inf. foll. ⓐ only rarely w. the
fut. inf., w. which it is regularly used in ancient Gk. (Hom. et al.),
since in colloquial usage the fut. inf. and ptc. were gradually
disappearing and being replaced by combinations with μέλλω (B-D-F
§338, 3; 350; s. Rob. 882; 889). W. the fut. inf. μ. denotes certainty
that an event will occur in the future μ. ἔσεσθαι (SIG 914, 10 μέλλει
ἔσεσθαι; 247 I, 74 ἔμελλε … [δώσε]ιν; Jos., Ant. 13, 322; Mel., P. 57,
415) will certainly take place or be Ac 11:28; 24:15; 27:10; 1 Cl
43:6; cp. Dg 8:2.
Arndt, W., Danker, F. W., Bauer, W., & Gingrich, F. W. (2000). A
Greek-English lexicon of the New Testament and other early Christian
literature (3rd ed., p. 627). Chicago: University of Chicago Press.
In addition to the cited passages in Acts, which are equivocal at best, he cites only two others, from other authors. Only the Clement passage seems to prefer a reading of "was certainly going to happen...":
1 AND what wonder is it if those who were in Christ, and were
entrusted by God with such a duty, established those who have been
mentioned? Since the blessed Moses also “A faithful servant in all his
house” noted down in the sacred books all the injunctions which were
given him; and the other prophets followed him, bearing witness with
him to the laws which he had given. 2 For when jealousy arose
concerning the priesthood, and the tribes were quarrelling as to which
of them was adorned with that glorious title, Moses himself commanded
the rulers of the twelve tribes to bring him rods, with the name of a
tribe written on each; and he took them, and bound them, and sealed
them with the rings of the rulers of the tribes, and put them away in
the Tabernacle of Testimony on the table of God. 3 And he shut the
Tabernacle, and sealed the keys, as he had done with the rods, 4 and
he said to them, “Brethren; of whichsoever tribe the rod shall bud,
this has God chosen for his priesthood and ministry.” 5 And when it
was daylight he called together all Israel, six hundred thousand men,
and showed the seals to the rulers of the tribes, and opened the
Tabernacle of Testimony, and took forth the rods, and the rod of Aaron
was found not only to have budded, but also to be bearing fruit. 6
What do you think, beloved? That Moses did not know beforehand that
this was going to happen? Assuredly he knew, but he acted thus that
there should be no disorder in Israel, to glorify the name of the true
and only God, to whom be the glory for ever and ever. Amen.
Clement I, P., Ignatius, S., Bishop of Antioch, Polycarp, S., Bishop
of Smyrna, & Lake, K. (1912–1913). The Apostolic fathers. (K. Lake,
Ed.) (Vol. 1, pp. 81–83). Cambridge MA; London: Harvard University
1 For before he came what man had any knowledge at all of what God
is? 2 Or do you accept the vain and foolish statements of those
pretentious philosophers, of whom some said that God is fire (they
give the name of God to that to which they shall go) and some water,
and some one of the other elements which were created by God. 3 And
yet if any of these arguments is acceptable it would be possible for
each one of the other created things to be declared God. 4 Now these
things are the miracle mongering and deceit of the magicians; 5 but
of men there is none who has either seen him or known him, but he
himself manifested himself. 6 Now he manifested himself through
faith, by which alone it is given to see God. 7 For God the Master
and Creator of the universe, who made all things and arranged them in
order was not only kind to man, but also long-suffering. 8 Nay, he
was ever so and is and will be, kindly and good and free from wrath
and true, and he alone is good. 9 And having formed a great and
unspeakable design he communicated it to his Child alone. 10 And so
long as he kept it in a mystery and guarded his wise counsel, he
seemed to neglect us and to be careless; 11 but when he revealed it
through his beloved Child, and manifested the things prepared from the
beginning, he gave us all things at once, both to share in his
benefits and to see and understand, and which of us would ever have
expected these things?
Clement I, P., Ignatius, S., Bishop of Antioch, Polycarp, S., Bishop of Smyrna, & Lake, K. (1912–1913). The Apostolic fathers. (K. Lake, Ed.) (Vol. 2, pp. 367–369). Cambridge MA; London: Harvard University Press.
Below are all of Luke's uses of μέλλω:
[Luk 7:2 YLT] (2) and a certain centurion's servant being ill, was about to die, who was much valued by him,
[Luk 9:31, 44 YLT] (31) who having appeared in glory, spake of his outgoing that he was about to fulfil in Jerusalem, ... (44) 'Lay ye to your ears these words, for the Son of Man is about to be delivered up to the hands of men.'
[Luk 10:1 YLT] (1) And after these things, the Lord did appoint also other seventy, and sent them by twos before his face, to every city and place whither he himself was about to come,
[Luk 13:9 YLT] (9) and if indeed it may bear fruit --; and if not so, thereafter thou shalt cut it off.'
[Luk 19:4, 11 YLT] (4) and having run forward before, he went up on a sycamore, that he may see him, because through that >[way] he was about to pass by. ... (11) And while they are hearing these things, having added he spake a simile, because of his being nigh to Jerusalem, and of their thinking that the reign of God is about presently to be made manifest.
[Luk 21:7, 36 YLT] (7) And they questioned him, saying, 'Teacher, when, then, shall these things be? and what >[is] the sign when these things may be about to happen?' ... (36) watch ye, then, in every season, praying that ye may be accounted worthy to escape all these things that are about to come to pass, and to stand before the Son of Man.'
[Luk 24:12 YLT] (12) And Peter having risen, did run to the tomb, and having stooped down he seeth the linen clothes lying alone, and he went away to his own home, wondering at that which was come to pass.
[Act 3:3 YLT] (3) who, having seen Peter and John about to go into the temple, was begging to receive a kindness.
[Act 5:35 YLT] (35) and said unto them, 'Men, Israelites, take heed to yourselves about these men, what ye are about to do,
[Act 11:28 YLT] (28) and one of them, by name Agabus, having stood up, did signify through the Spirit a great dearth is about to be throughout all the world -- which also came to pass in the time of Claudius Caesar --
[Act 12:6 YLT] (6) and when Herod was about to bring him forth, the same night was Peter sleeping between two soldiers, having been bound with two chains, guards also before the door were keeping the prison,
[Act 16:27 YLT] (27) and the jailor having come out of sleep, and having seen the doors of the prison open, having drawn a sword, was about to kill himself, supposing the prisoners to be fled,
[Act 17:31 YLT] (31) because He did set a day in which He is about to judge the world in righteousness, by a man whom He did ordain, having given assurance to all, having raised him out of the dead.'
[Act 18:14 YLT] (14) and Paul being about to open >[his] mouth, Gallio said unto the Jews, 'If, indeed, then, it was anything unrighteous, or an act of wicked profligacy, O Jews, according to reason I had borne with you,
[Act 20:3, 7, 13, 38 YLT] (3) having made also three months' >[stay] -- a counsel of the Jews having been against him -- being about to set forth to Syria, there came >[to him] a resolution of returning through Macedonia. ... (7) And on the first of the week, the disciples having been gathered together to break bread, Paul was discoursing to them, about to depart on the morrow, he was also continuing the discourse till midnight, ... (13) And we having gone before unto the ship, did sail to Assos, thence intending to take in Paul, for so he had arranged, intending himself to go on foot; ... (38) sorrowing most of all for the word that he had said -- that they are about no more to see his face; and they were accompanying him to the ship.
[Act 21:27 YLT] (27) And, as the seven days were about to be fully ended, the Jews from Asia having beheld him in the temple, were stirring up all the multitude, and they laid hands upon him,
[Act 22:16, 26 YLT] (16) and now, why tarriest thou? having risen, baptize thyself, and wash away thy sins, calling upon the name of the Lord. ... (26) and the centurion having heard, having gone near to the chief captain, told, saying, 'Take heed what thou art about to do, for this man is a Roman;'
[Act 23:27, 30 YLT] (27) This man having been taken by the Jews, and being about to be killed by them -- having come with the soldiery, I rescued him, having learned that he is a Roman; ... (30) and a plot having been intimated to me against this man -- about to be of the Jews -- at once I sent unto thee, having given command also to the accusers to say the things against him before thee; be strong.'
[Act 24:15, 25 YLT] (15) having hope toward God, which they themselves also wait for, >[that] there is about to be a rising again of the dead, both of righteous and unrighteous; ... (25) and he reasoning concerning righteousness, and temperance, and the judgment that is about to be, Felix, having become afraid, answered, 'For the present be going, and having got time, I will call for thee;'
[Act 26:2, 22-23 YLT] (2) 'Concerning all things of which I am accused by Jews, king Agrippa, I have thought myself happy, being about to make a defence before thee to-day, ... (22) 'Having obtained, therefore, help from God, till this day, I have stood witnessing both to small and to great, saying nothing besides the things that both the prophets and Moses spake of as about to come, (23) that the Christ is to suffer, whether first by a rising from the dead, he is about to proclaim light to the people and to the nations.'
[Act 27:10, 30, 33 YLT] (10) saying to them, 'Men, I perceive that with hurt, and much damage, not only of the lading and of the ship, but also of our lives -- the voyage is about to be;' ... (30) And the sailors seeking to flee out of the ship, and having let down the boat to the sea, in pretence as >[if] out of the foreship they are about to cast anchors, ... (33) And till the day was about to be, Paul was calling upon all to partake of nourishment, saying, 'Fourteen days to-day, waiting, ye continue fasting, having taken nothing,
[Act 28:6 YLT] (6) and they were expecting him to be about to be inflamed, or to fall down suddenly dead, and they, expecting >[it] a long time, and seeing nothing uncommon happening to him, changing >[their] minds, said he was a god.
So if not biased, it seems somewhat unfair to characterize Luke's Koine as colloquial and he the three NT uses of the exact phrase can, and I think should, be read as "about to".