Andrew - Thanks for the reply and great point. Not "digging in" might definitely be a better goal that not "touching." And that's probably a better way of describing where squarewaves fall for me.
I've tried really thick grips, and absolutely agree that a thinner grip helps me relax my hands more.
Maybe the reason I love the squarewave shape so much is that my hands are on the larger side given that I'm a little over 6'1", so the middle diameter feels good (and gives me some cushion in that area of my palm), but I'm still get the feeling of 29ish mm diameter with my pinkie.
Thinking about the renthals some more, what I didn't get along with was the lack of cushion in the middle more so than the small diameter all the way across the grip. Maybe I'm leaning on my bars too much on longer rides on rolling terrain, which could be a combo of lack of core strength and modern geo.