[ $7 Spin ] TPTK vs. Maniac

Villain is a maniac that never stops betting for no reason, my question isn't about rather I was ahead or not. In my head the only way he's ahead is in a cooler, just a couple hands earlier he went three streets bluffing with 9-high on a AsQs8d board.

My question is: Is this the best way to extract full value in this spot?

Poker Stars, $6.58 Buy-in (10/20 blinds) No Limit Hold'em Tournament, 2 Players
BB: 760 (38 bb)
Hero (SB): 740 (37 bb)

Preflop: Hero is SB with K J
Hero raises to 40, BB calls 20

Flop: (80) T J 7 (2 players)
BB bets 40, Hero raises to 113, BB raises to 260, Hero raises to 700 and is all-in, BB calls 440

Turn: (1,480) A (2 players, 1 is all-in)
River: (1,480) 3 (2 players, 1 is all-in)

Results:

Spoiler

1,480 pot
Final Board: T J 7 A 3
BB showed 7 2 and lost (-740 net)
Hero showed K J and won 1,480 (740 net)