Playing middle set on a wet board multi-way?

Ignition - $0.10 PL Hi (6 max) - Omaha Hi - 5 players
Hand converted by PokerTracker 4

UTG: 100 BB
CO: 19.2 BB
Hero (BTN): 106.4 BB
SB: 83.9 BB
BB: 74.9 BB

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has K♦ 7♥ 7♣ K♥

UTG raises to 3.5 BB, fold, Hero calls 3.5 BB, SB calls 3 BB, BB calls 2.5 BB

Flop: (14 BB, 4 players) K♣ A♦ T♦
SB checks, BB checks, UTG checks, Hero bets 10 BB, fold, fold, UTG calls 10 BB

Turn: (34 BB, 2 players) 4♥
UTG checks, Hero bets 32.3 BB, fold,

I thought about 3-betting preflop, but double-paired hands do better multiway, so I called.

I flop middle set. I block the NF, which would support checking back (because I block opponent's calling range). However, we're multway and I unblock JQ, so there are lots of straight draws out there.

Should I bet full pot when the turn bricks?