Have no SD value, but have many outs. _open ended oop

Firstable, take advantage of statistics: check fold to c-bet. If you play against UNK, I would always c-bet here. He should insta fold 22, 33, 55-TT, missed Ax. Your equity is too strong to check in my opinion.
In fact 8 cards OTT give you nuts, 6 cards at least showdown value.
For me this is bet, bet.

You only have a drawing hand otf. If you check, the pot will be small. If Villain has TP or better, he will bet flop and turn, and since you have no sd value, you will have to fold otr unimproved. If you hit, you will get one bet, perhaps two. If Villain has a draw, he might check.

So i think you should bet 2 streets. He can fold a lot of better hands. And he can call some worse hands. Perhaps you can even bluff otr. And if you hit a 9, a calling range of BTN might hit 2P or set and pay a complete stack. Seems to me that there is more EV in betting.

Cbet smaller, 1/3 would be ok and then bet 2/3 - 3/4 OTT.

Why this smaller sizing? (cause I bet for folding 22-TT and he fold them on this sizing too?)

You can not do anything else. Wp