We will still be in slightly EV favor, so imo the small cbet is fine.
Turn/river seem kind of interesting. I guess MP will have more 6x and 3x in his range than us, but not too much.
I honestly ran this through wizard and it prefers one of two ways:
Either we check it down for SDV (even though we will often split the pot) or we triple it off with out strong blockers to Qx.

Three barrels or one, i agree, villain dependent. I mostly give up but i know a folder or two

On a dry board like this, and with blockers to AQ and KQ I would fire two barrels. Flop cbet I think is good. Turn I would bet 3/4 to full pot. If called on turn and my hand doesn't improve I would check fold.

Our 3b range is very narrow here. We have AA/KK/QQ/AQ/KQ/QJs/QTs. We are probably supposed to be here 50 to 60% (could be wrong). I am pulling most of my bets out of the above range and maybe thin vs betting/bluffing JJ/TT/99. They can turn nutted and wont' complete anything on the very bets turns where we make sets.

Or maybe look at our AKs range specifically on this board and look to check/decide the AKs and bet with the BDFD's.

Pool kind of sucks when they call 3 bets so a pool range can look drastically different than some chart base calling range MP vs SB.

As for bet/bet, I think that 6 has zero effect on equities here since neither one of us has any 6's. If someone did have 6x, it should be us with 76s or 65s. Not a spot I 3b A6s. As for him, I guess he can have a combo or two depending on how bad he is. I am inclined not to want to bet/bet because I don't think he folds enough then we get to river in a bad spot.