Flatting pre is good. Considering ICM issues he probably won't call you often. The problem on shoving is that he is never paying you with a draw, given ICM, and you block a lot of the combos that he is calling, at minimum AJ. I know that kinda sucks to see him check behind the river very often on this texture but the fold equity OTT is so high that you are actually not maximizing your EV on shoving. A tank call and checking river is better, hoping that he finds some way to fire a bullet with KcQc or something. 

The problem on x/r flop is that you can not have the nuts on a standard way to play (ok you have but whatever) that is to 3b pre. The 7 turn is better for your range but in terms of overall range, are you shoving as a bluff very thin there, to show a good shove with AA. 66 I like to x/c and lead on this texture, given that A high boards he won't barrel so relentlessly and a 7 is good for our range. To balance 66/J6, I would lead as bluff 98, QT, some low suited clubs.

Flat is nice, but c/rip turn is spewy imo since you block everything, i would just keep ch/calling any rivers

I'd shove pre here. You should be reshoving wide here to punish him on the bubble taking out AA is not great for our range. As played i'd either c/c down and hope to induce bluffs or bet/bet and try to induce hero calls. Villain should have very hands that are so strong he needs to stack them off here. Checking lets him pot control his medium strength hands and check shoving allows him to fold his bluffs. You don't want to prevent him from bluffing and allowing him to pot control.