Thoughts on this hand?

Playing 2/5 Zone Poker. I'm dealt 6s7d in the big blind. I have about 2500 behind, UTG has about 660. UTG raises to 11, SB calls, I call in the big blind.

Flop comes 8c9h4c. UTG bets 15.68, SB folds, I call. Turn comes 5s giving me the nut straight. UTG puts in an overbet of 76.7 and sitting with the nuts I check raise to 168. UTG calls and turn comes 5c. UTG calls for 91 more.

River comes 5c so board is now paired (8c9h4c5s5c) and I no longer have the nuts. Flush draw gets there (unlikely) but opponent can now have a FH.

I decide to check and villain shoves all in for about 417. I'm thinking with overpairs, top pair, etc. you'd expect them to check back for showdown. I only have about 30 seconds to make a decision online and end up folding when time expires. I ended up losing about 200 bucks but REALLy wanted to call. There are no bluffs at that point... right? Was this the correct play?