I'm unsure of a range for villain here and I simply played the hand as I would any MP+NFD.

I belive however I played it badly and wasn't getting the equity needed, it's fairly marginal.

Full Tilt Poker, NL Hold'em Tournament, 40/80 Blinds, 9 Players
LeggoPoker.com - Hand History Converter

CO: 6,305
BTN: 2,445
Hero (SB): 2,810
BB: 3,675
UTG: 2,550
UTG+1: 13,615
UTG+2: 4,315
MP1: 2,720
MP2: 2,170

Pre-Flop: (120) K 7 dealt to Hero (SB)
UTG calls 80, 2 folds, MP1 calls 80, MP2 calls 80, CO calls 80, BTN calls 80, Hero calls 40, BB checks

Flop: (560) 7 4 A (7 Players)
Hero checks, BB checks, UTG checks, MP1 checks, MP2 checks, CO checks, BTN bets 320, Hero calls 320, 2 folds, MP1 raises to 1,120, 3 folds, Hero raises to 2,730 and is All-In, MP1 calls 1,520 and is All-In

Results: 6,160 Pot

Just check shove the flop. Btn is probably calling you often (unlikely he bet into so many players without SOMETHING) but a lot of the times he has worse flushdraw and you are flipping lots so just shove it. He folds like a donkey sometimes too.