Interesting mob, all chanting do it, do it, do it!
I don't think anyone answered your initial thought in all the boostering. Other than what azgjav said, a solid backed choice - which would match all the parts you have now. Turn it into a Base or different sub dialed model that matches it's current age, [the first would cure the recess without changing the existing movement.]
Still noting the 111H desire. just pick one up full-fledged. With a CN motor they are pretty cheap now. You will get the newer case and back, the AR and all the other wants - except for the recess, all the 111H's have the glaring RECESSED CANON, which is where your upgrade then comes in.
Buy a Davidsen CN6497 and swap it with the OEM. That gives you a very clean 111H and a backup movement. You get all the modern details of a 111H as well it has no recess and so actually looks like a GEN. (Which is the reason to buy a 111H in the first place?) No swan of course, but the front of the watch sells the illusion.
Or, sell the one you have, it's Swiss after all and should fetch you a good amount of the funds to purchase a new 111H and the upgrades to fit your needs.