Re: Which Stays In Tune Better?
Lighter gauges are considerably floppier, but I don't think they are less stable because of the reduced tension and gauge. Strings are designed to be played so in general they should perform well and overstretching and giving them aerobics sessions don't reflect what you do to them when you play them. Even when incorporating heavy Floyd use you're not stressing out an individual string, but all of them together.
I'd suggest checking for nut slot binding since this guitar is not a trem guitar, you're most likely to have nut problems. Is that a generic/replacement nut or a custom nut? What shape are the slots, U or V? Is the low E at least 1/4 out and free of the slot and the rest of the nut radiused and shaped correctly? Is nut action okay (a 0.50mm pick should just barely fit between an open string and the first fret)?
On most custom nuts people tend to hurry with filing, especially on bone nuts that take a long time to file, and that creates chatter marks. Finishing the nut slots with a couple of firm and steady strokes eliminates possible bindings. Bone nut tends to heat up as you're cutting the nut slots, and as it does the nut slot narrows and your file starts to bind and skid.
Do you do the top wrap technique? Since it's nothing wrong with that at all, some string types don't work so well. If you see the end of the string which is wound thicker at the ball end sticking out of the tailpiece too much and won't take the shape of it, that might be inducing tuning issues too so make sure that the string comes clean out of the hole if you top wrap.
Tuning issues on a proper guitar are almost exclusively a mechanical problem. Some guitars have inherent tuning problems, 3+3 HS types that put the string at whacky angles because the designer never really cared about how strings travel to the tuning posts past the nut, but that's another story and does not apply for a PRS.
And make sure you check everything, take your time. Take off the tailpiece/bridge and check the bushing if the are seated nicely, tighten your tuners, lube your nut, leave no stone unturned.