I like it in particular here, since villains range should consist mostly of PPs that could find a stab along with other pair+draws.

I like the OOP check but more from an exploitative standpoint. BTN will be stabbing too often. And we have a decent amount of showdown hands that want to get there cheap. I wouldn't simplify here and go range check though. This board gives us a solid advantage and I would try to drive it home by having a decent betting range for a decent size.
This hand seems fine as a check as it's less likely BTN has a showdown hand that he won't bet blocking the T. Check raise for value is fine.

Looking at the range given above, think we have healthy equity to bet big again and charge most of his draws.

Seems good. There is KQ, QT, JQ, and even worse made hands such as JT that we are getting value from. Seems solid.

We need to call 19.17 to win 57.61. Your 33% is on the mark, it's 33.28%.
I've been playing around with the hands you have posted. It seems to depend on how often BTN is bluffing.
Range: TT,KJs-KTs,Q9s,JTs,98s,AdJd,QdJd,Ad9d,Ad8d,KJo is very value heavy. It has some bluffs in Ad9d, Ad8d, AdJd, QdJd we are not calling. When I add three combo's nut flushdraws Ad5d-Ad3d then this already becomes a breakeven call.
This range does not contain AQ in BTN's range. For every 2 combo's of AQ BTN would need to add about 1 combo of AdXd bluff to keep us interested in calling.

Might be worth more to look at your own range and see that way if KT needs to be called or can be folded. We don't block bluffs but we also block hands that we beat. And not blocking straights. We have straights, sets, better 2 pair. Maybe it's not needed to call this but unsure about your range.