PLO25 TT98ss max value from quads

I agree with all your actions and thoughts in this hand.
I also think that check-raising gives most value on the river. (like you said also a lot of Jxxx hands are betting on the river as well)
Best case is BU slow playing a full house and calling your check-raise, mmedium case is BU bet-folding (which still gives a little value) and worst case BU checks behind.

If he has JJ, it doesn't matter what you do. The stacks go in.

If he has 88, he might check it back, and he might fold it to check-raise. So it's like sometimes you miss value by betting, sometimes you miss value by checking.

So we can skip those two hands, and focus on how to get the most value from his non-JJ/88 hands.

When you bet flop and barrel turn, his range is polarized to bluff catchers and missed draws. Versus weaker made hands you get more value by betting, versus missed draws you get more value by checking (and letting him bluff).

Even if he calls flop with draws, his range is heavily (75/25) weighted towards J+ on the river. So even if he is bluffing all his missed draws, it would be better line to go for smaller value bet. As said, if he has JJ the money goes in. He has 88 about 1% of times (you block it) so pretty much all his non-JJ made hands are not really strong. I would go for slightly over half a pot sizing there.