Once was from blind position, the other two times from IP against EP raise, LP 3b.

Curious to know why you don't have JJ in your initial analysis? I personally would 3b JJ on the button, but I see plenty of people who see a flop and then start playing it when no overcards come (in fact have won some nice pots with KK/AA from guys who thought their jacks were good on a low flop).
A slow played top set is also commonly seen here

I had similar Eq calculations to you but didn't have T8s as often and JJ more.

So the play from here went on as:

Hero calls

River 7 clubs

Hero checks, BTN bets all in (~260BB)

Thoughts on his range now?