Should hero bet this flush-completing turn given the high hand bonus implications?

Had this hand at my local 2/5 game last night.

PREFLOP

UTG+1 limps, lojack limps, hijack limps, hero in the cutoff raises to $35 with K♦T♦. UTG+1 folds and the other players call. Hero has $1300, lojack has $800, hijack has $900.

FLOP ($105)

Q♦9♦4♣

The action checks to hero, who bets $40. Lojack folds and hijack calls.

TURN ($185)

Q♦9♦4♣7♦

Hijack checks. Hero...?

The reason why there is any debate here regarding what would otherwise be an obvious value bet is because there is a $1000 high hand bonus for a king high straight flush at this casino. My odds of hitting it on the river are 45 to 1, which I assume increases the EV of checking by about 1000/45, or around $22.22.

I guess one way of solving this would be to check with a solver what the EV of betting is for hero at various different sizes, and then compare it to the EV of checking. Obviously hero has a very high EV bet here, probably in the region of $160, assuming a reasonable bet size is used. However, I expect the EV of checking to be pretty similar, in all likelihood maybe slightly lower, like $155 or so (but these are just estimations and I have not checked yet with a solver). If the above was true then checking would clearly be significantly higher EV and should be chosen every time, right?

Presumably this is also true on the flop in such situations, and to an even higher degree, as the various options are going to be lower EV on the flop as the pot is smaller?

Any thoughts/input/feedback/criticism appreciated.