Online 2/4, 100 deep, no HH unfortunately.

We open KcJc from the HJ to 9, CO 3bets to 27, we defend.

Flop Td9c4c, so we have overs, a gutshot, and a flush draw.

We check, he bets 20 into 60, we make it 95, he calls.

I have 8 value combos - 6 sets, and 2 x 2 pair. So I figure c/ring 87s, QJs and KJs is good, that'll be 12 combos of bluffs.

Turn is a 4.

On the turn, I ended up shoving, but this where it gets tricky. He should know that we have plenty of potential bluffs, and still only 8 value combos, so its easy to overbluff here. But if we check we have to check/fold. So should I just shove my highest equity bluffs, and check the rest hoping he gives up?

I presume betting small isn't an option since we have polarized ourselves on the flop. Any feedback much appreciated.