$0.05 / $0.10 100BB stacks, Hero in BB with Kh Jh Td 5d, Villain (no stats) opens BTN for $0.30, SB folds, Hero flats.

(Pot $0.65)
Flop Ah Th 9c

Hero flops Royal Flush Gut draw, Nfd, Gutter and Mid pair. What is the best line to take against an unknown typical BTN range here?

Here's what ended up happening:
Hero checks, Villain bets $0.50, Hero x/r's to $2.95, BTN pots $6.55, Hero shoves and loses to AAxx on brick run out.

Because of the massive sizing villain used, me having the Nfd and some straight blockers it was obvious Villain had a set.
With Villain only having $2.65 left after potting and therefore being committed, I felt I had to shove with about 36% equity against his set, basically having to put in $6.75 more to win $20 or needing only 25% equity for this to be profitable (is that calculation right?).

Should I check call flop or will I lose too much equity if it's a blank turn and be forced to x/fold on the turn? Or does it make sense to try and improve before shoveling more money in since the SPR was 15 on the flop? Thanks.