The black bars ARE only 2 black bars per boss, per party, not per person, yes. However, they are considered white drops. So once you check the loot with you or whatever alts you're with in the party that actually GOT the black bars, close the loot interface without looting the black bars, and you "should" be able to pick up the black bars with any character in the party.
I have not run into that issue yet or the issue of not being able to turn in the black bars to the npc's. The only issue for me so far has been for two days (two runs) in a row now, for me anyways, at least one mini boss on Boss 2 hasn't dropped black bars. Which must mean that they (while having a very high percentage) are not 100% guaranteed drops from the mini bosses. If it was JUST Snow Blake like my initial hypothesis being that someone else had the same issue with Snow Blake, that would tell me it's a possible bug with Snow Blake. However, after having Snow Blake drop black bars, and having Ancalon (who previously DID give me black bars) NOT give me black bars, tells me its probably just not a guaranteed drop, however unlikely and unlucky of a scenario it is.
For me, it was twice in a row.
Wish I had that kind of consistency when pulling stats lol..