Extracting maximum value from a set deepstacked, multiway, out of position, with flush draw on board

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Extracting maximum value from a set deepstacked, multiway, out of position, with flush draw on board

Blinds: t40/t80 (8 Players) SB: 9,178
BB: 9,653 (Hero)
UTG: 7,487
UTG+1: 9,089
MP: 16,531
MP+1: 9,992
CO: 6,300
BN: 10,218
Preflop (120) Hero is BB with 9 9
4 folds, CO calls 80, BN raises to 400, SB calls 360, Hero calls 320, CO calls 320
Flop (1,664) A 3 9
SB checks, Hero checks, CO checks, BN bets 832, SB calls 832, Hero raises to 2,400, CO folds, BN folds, SB folds
Final Pot BB wins 4,160

I'm so unsure what to do on the flop in this spot!

We have many options:

1)Donklead
PROS: We know that an ace is never folding to a Donklead on the flop. We could take the lead on the flop and bet out the three streets out of position.
CONS: We miss value from cbet-bluffs, if nobody has an Ace the hand will probably end on the flop with no more chip extraction. Also we give correct odds for the flush draw.
It's difficult to balance vs good players, since I don't see myself donkleading with air or with flush draw, since it is so likely that at least one of them have an Ace and won't fold.

2)Check/call
PROS: Disguises the hand. Also mixes (balance) with what I think I should do with a flush draw: having a strong flush draw, I'd just call to keep the pot multiway on the turn in order to maximize my implied odds when I hit the flush.
CONS: Holding the actual trips, we risk seeing another heart on the turn, which in the worst case could lead us to loose a big pot, or in the best case to minimize our chip extraction, because people will fear the flush.

3)Checkraise all in (>2x pot overshove)
PROS: Makes it easy to play the hand, eliminating the positional disadvantage. Could be interpreted as a
draw or some sort of sick bluff, and could get calls from good Ax hands . Gives incorrect odds for people holding the flush draw to call.
CONS: Some people might actually fold good Ax hands like AQ/AK to this huge bet. Also stops the aggressor from bluffing later streets.

4)Checkraise to 2400 (like I did in the actual hand)
PROS: Doesn't look so massive like the overshove. Should keep the flushdraws on the pot, maybe can induce shoves by them. People holding 2-pair will also likely shove. Sometimes people holding AK/AQ will still continue, but not many times.
CONS: Looks extremely strong in a 3bet pot vs 2 people that already showed interest in an A-high flop. Looks exactly like what it is: a flopped set. Could get folds by people holding a hand as strong as AK.

CONS for all "check" options: It could be checked down to a turn and we risk giving a free card to the flush drawer.

Any thoughts? So many options, all with their pros and cons... which line should be best vs different types of opponents?

Thanks!

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