I almost wonder if we have enough equity to call here just based on enough Axcc stuff in his range.

No reason to wonder......sounds like you have some stove homework. (I should do the same although I don't think we do)

I've done some, and I get anywhere form 8% (too optimistic) to 4% (perhaps a bit too pessimistic) so to be honest.... it's really really close. it really just becomes how much Axcc you put in BB range....

wrt the river:
So much to process on this, but I'm most inclined to put him on 33, 55, 46, even T7. With BB's stats pretty much out of the window given his position, it's typical to wait for the turn to pound with a set. The straight draw came in on the turn. T7 gives him 2pr. Plus we have the kicker issue. There's also QT and AT but probably less likely given there was no 3! on the flop. Unless he has shown himself to be a spazz on the river, I'm inclined to c/f.

wrt preflop & flop
I'm not usually as aggro as others and I certainly make some bad calls that sometimes end up good. I will cool call suited connectors in the blind, but rarely never c/r the flop with a draw to a middling flush.