The movement in your watch is a 2813, if you really want to upgrade your watch you can do so with an Eta clone 2836-2. You will need to replace the dial feet, get new eta hands and a movement ring. The date window on your dial is in the eta position.
Yep. I put gen Etas in my favorites, though I have lots of watches with clones. If and when a clone has problems, I will just replace it for $70, easier and cheaper than the headaches from trying to fix them.
I've found that gen ETA replacement parts don't always mesh with clone keyless parts, you'll probably have to replace the entire keyless works. The date wheel issue is another matter, the keyless cover should hold it in place.
I would try adding some tension to the spring on the setting jumper, perhaps the hacking lever is causing the stopping. No idea about the date wheel...
I with you man. All reps are fantasy when you get down to it, so why not build to your own tastes, it IS your watch after all. It's called "bespoke customization" in any other realm.