^ I’m among the people who believe locking tuners don’t contribute one iota to tuning stability. Bridge and nut are usually the culprits. So, I’m inclined in agreeing with you in that you’d have gotten stability just with what you did to the bridge.
Op, since you are messing with the pivot screws, it’s imperative that you get them absolutely right. Fractions of a mm off and your guitar won’t stay in tune. Widen the slots of the nut. Wrap each string in a thin sandpaper to use it as tools if you don’t have access to nut files. Just don’t put pressure down, as you don’t want to change the height of the strings at the nut. You won’t need to widen too much either, just enough to accommodate the wider gauges without causing any binding at the nut. To apply graphite at the nut use a mechanical pencil. I’ve used all sorts of things before, but graphite applied with a mechanical pensil has been the best approuch even on guitars that are notorious for going out of tune. My Gibson guitars are just as stable as any of my PRSi using the graphite method and making sure the slots weren’t pinching the strings.
As for your rant, I understand the frustration. However, it is clearly a setup issue, not an inherent issue with the guitar itself. You put a thicker string gauge on that guitar, which in turn requires you to make some adjustments. You changed the bridge, which also requires you to set up the new bridge properly. Adjusting the pivot screws on that bridge requires a lot of patience and precision. When I say I understand the frustration is because I’ve been there with a CE24 and ended up regretting selling the guitar. It was clearly a bridge setup issue or possibly the bridge still needed it’s breaking in period. Which by the way, since your replacement bridge is brand new it might also need some time to break it in. Again this is not a PRS thing, as every strat I’ve ever had needed to be broken in as well.