So I tried a thumbless grip for the first time ever today during a set of overhead presses and the difference was remarkable, not only in the tension on my shoulders but also in strength.
I was fairly nervous throughout at the prospect of dropping 185 on my head, but as the set went on I noticed that my form was much better than when I use a thumbwrap and my wrists, elbows and shoulders felt more stable as a result. A bit of chalk probably also helped.
I realize that it’s probably not a good idea in theory, but in practice it seemed to work very well. I also wouldn’t try it when maxing my bench, but other than that I think I may start using this more often.