I'd like to go and make it $3.90 or so. A river shove looks super strong and nutted, and there's a good chance villain does not have a super strong hand (60vpip plays too many hands) so they are folding a bunch.

I prefer your line when there's quite a few missed draws. Here though it just looks too nutted and will be much worse EV than a normal size bet.

As there's not too many strong hands villain will call three barrels with I would bet a non polarising amount around $2.40 hoping he somehow gets here with Qx or has 87. This villain type won't always raise his sets on the flop or turn so we can still expect to get the money in on the river some % if he does have one.