First of all, remember that this is poetry, erotic poetry, and the writer's intent is to be slyly suggestive, so trying to nail down a precise single meaning is not going to be super productive.
Secondly, you should have backed up and asked what the prepositional mem (מ) "from" is doing before menishikot (נשיקות) in verse 2. What does "from the kisses" or "more than the kisses" mean!? The verse would be simpler without the mem as in Proverbs 27:6:
נֶאֱמָנִים פִּצְעֵי אוֹהֵב וְנַעְתָּרוֹת נְשִׁיקוֹת שׂוֹנֵא
Looking at verses 2 and 3 we see the following paired alliterative balance:
- verse 2: מִנְּשִׁיקוֹת, מִיָּיִן
- verse 3: לְרֵיחַ, עַל כֵּן עֲלָמוֹת
That is, two mem expressions in verse 2 followed by three lamed expressions in verse 3.
The second mem, before yayin (יין) "wine" is clearly a comparative, meaning "more than" wine. Since wine is itself a superlative figure, this is a super-superlative expression. When you get to the the end of verse two, and look back at the beginning of the verse, you are left with the feeling that the first mem, which at first glance looks superfluous, might also be intended as a comparative and the suggestive reading is therefore
Let him kiss me more than his kisses, for your love is [more] better than wine.
The mem and lamed prepositional prefixes are often opposites, denoting "from" and "to". There is a hint of this in these couplet verses 2 and 3. Verse 2 is "from" and "more than", and verse 3 is "to" or "for".
The cantillation indicates that לְרֵיחַ שְׁמָנֶיךָ טוֹבִים is an independent phrase. This implies that the literal translation is as rendered by Young's Literal Translation and the meaning in current American usage is
Your [perfumed] oils are great for (ל) fragrance,
[As] for [your] fragrance, your [perfumed] oils are great
Think of this as "Your aftershave thrills me".
The author of Song has changed the normal word order to put the lamed prepositional "for fragrance" at the beginning of the verse so that the placement of the lamed alliterations in the verse matches the placement of the mem alliterations in verse 2.
Verse 3 has an additional alliterative pattern based on the the letter pair shin-mem ; שְׁמָנֶיךָ, שֶׁמֶן, שְׁמֶךָ "your oils [perfumes]", "oil", "your name", reminiscent of a similar alliterative pattern, טוֹב שֵׁם מִשֶּׁמֶן טוֹב, in Ecclesiastes 7:1 (KJV)
A good name is better than precious ointment;
Therefore, in verse 3, the next phrase, שֶׁמֶן תּוּרַק שְׁמֶךָ is also independent, the literal translation being
Your name (reputation) is [as] oil poured out
and the intent in current American usage is
You are the very image of opulence, and that's why the bachelorettes are crazy about you
Note that there are no "virgins" (בטולות) in these verses, only young women (עלמות).