Also fighting a compressed thumb ligament in my left wrist so it's tough to get a good support hand grip.
There are a number of different grip styles and approaches, a couple of which don't need support-hand thumb pressure at all. Run a youtube search for "handgun nut cracker grip" to see if something comes up.
Short version: you're wrapping your support fingers over your strong fingers to kind of lock them in like a fulcrum or a hinge pin, while pressing into the gun's grip with your palms/heels. Left thumb is somewhat relaxed and often not even touching the gun at all. Lock your wrists back as part of that, with generally even pressure left/right in pressing your heels into the grip - it almost feels like you're trying to pull your knuckles away from each other, but they're locked in and it's actually tightening everything down through leverage.
You're also not hulking down on the grip, trying to eliminate recoil - you're just managing and mitigating its effects as consistently as possible while the gun cycles and you focus on the target, sight alignment, and trigger press. This grip, in my own experience, simply allows for the most consistent shooting at speed, and across long strings of fire.
Part of the consistency I get out of this grip comes from how it helps isolate the trigger finger's entire structure away from unwanted inputs into the gun. Especially at speed and under pressure - I haven't found a better one in mitigating crap trigger presses. Which means, it's been the best so far in assisting in the most consistently good trigger presses. Largely because it changes the biomechanics of what's going on inside your hand with your firing hand's muscles, ligaments, flesh, etc, especially the trigger-finger's entire system, all the way up into the wrist. It isolates all of that more effectively. Other grips result in variations of pressing that trigger-finger and its components in the palm harder into the top of the gun's grip, which actually magnifies unwanted inputs - often resulting in shots going left, and the sights tracking in a kind of elliptical orbit rather than straight up and down. This grip results in extremely good, consistent vertical sight tracking, and better trigger presses under pressure.