Hero button with 78o flat.multiway pot on the flop.
FLOP:769r,check down to me.I elect to bet 1/3 pot 80,sb raise to 180,bb cold call,i call.Total pot 780.
TURN:Kh(backdoor flush),check all the way down.
River:Jd,sb check,bb check,hero how?

Apparently(maybe not),the guys before me acted as if they wanted a showdown.So,the pot is 780,i got 528 behind.Should i shove to make them fold to my exploitative play?

I chose to check back in reality.But i think,if the guys before me showed weakness,there is definitely a choice for me to make the best if it,isn't it?
My doubt is mainly that,since i have showdown value(i knew a pair of 7 basicly won't win the pot in a big chance),is this situation calls for a exploitative way by shoving the river,or,just safe play,check back?What will GTO elect to do in this river situation?What is the drawback of playing exploitatively in this situation（maybe get punished by one of them call,if they are sophisticated player which i think they are not.And little chance one of them will call in my perspective,except they suddenly decided to act irrationally or wildly.:)）