Global Poker 10NL - Shortstack spot with KJs

I'm 35bb deep. I open to 5.5bb from UTG+2 with KJs. Only MP calls. MP has me covered, but not by much (not that it makes much difference).

Flop comes T87r with one of my suit. Pot is 12.5bb. I cbet 6.25bb. MP calls.

Turn comes 2 giving me a flush draw. Pot is 25bb, so I have a little less than a PSB behind.

If he folds to a pot-sized turn bet 50% of the time I break even. If I end up winning the hand when called 33% of the time I break even.

With two overs and a flush draw, I doubt I have 33% equity here. My J outs might not even be clean outs. If I give him a flatting range of 22-TT, connectors KQ-65 and big-but-not-huge aces i.e. AQ-AT, almost that entire range is ahead of me, and not a large percentage of it is folding to a pot-sized turn bet.

I have to confess that at game speed I didn't notice that the flop c-bet left me with about a PSB behind if called, I just kind of autopiloted hoping he'd fold. I also didn't even think about how hard that board SMASHES a preflop calling but not 3-betting range.

Can I check-call a half-pot turn bet? I only need, what, 25% equity to break even? I'd have to be REALLY unlucky not to have 25% equity on that board. But I'd have to fold after putting about 75% of my stack in the pot if I don't improve. Not exactly the ideal situation with a short stack.

I'll stop there, I don't want to overcomplicate the discussion.