See that all 6 screws that fasten the bridge to the body are at the obsessively same height. Those screws have grooves around them (above the threads and below the heads) which serve as the fulcrum point(s) for the bridge. If they are not all in perfect (enough) alignment, trouble will ensue.
They are set at the factory at a height that floats the bridge about 2mm above the body, for about a half-step of up-bend. That's a good height, and I have no reason to change it - but if has been changed, then make sure the screws are ... see first paragraph. I find on most of the PRSeses I've handled, that the bridge-mount screws have been left alone (which works for most people). But I come across others...well, one can never be sure what a tech (or owner, if it's a used guitar - which I don't think yours is, just sayin') might have done in the name of setup. So a thing to check.
But as everyone says, grabby nuts are the A-number-1 cause of tuning issues. Short of having a master setup tech personally obsess over the nut for each player, taking into consideration the player's string choice, left-hand fretting force, right hand string-attack fury, propensity to bend strings, and tremolo habits, it's really hard to produce guitars with nuts that work for everyone.
Have some sympathy for the manufacturer who must mass-produce guitars that will travel the world and then, with a minimum of out-of-the-box setup, work for both a new player and a seasoned player, a light player and a heavy player, a fingerpicker and a dive-bomber - all of whom might get better results with a custom-tweaked nut than with a stock setup.
(Most brands will leave nut slots a little shallow and less than fully dressed, on the indisputable theory that it's easier for a tech to take material away later than to add it back - and because no one wants to get a new guitar out of the box and have the strings buzz down in the cowboy chord position.)
PRS, on the other hand - at least from the dozens of guitars I've been intimate with - really tries to dial the nut in, and in my experience usually get it purtnear right. But Perfection is a hard, uncompromising, and sometimes fickle mistress.
I think I understand that most SEs ship with 9s and most S2s (and on up the food chain) ship with 10s. Theoretically, the nut has been cut, grooves angled and dressed for the strings that ship on the guitar.* [See tangent below.] But I can't swear to that information - and if, frinstance, your guitar was set up for and shipped with 9s, and you put on 10s, there you go. When I change strings, going to 10s, I almost always have to address all the slots, widening (NOT deepening) them for the bigger gauge. This may not apply to your guitar, but it's still to be considered.
If, as an example, you go all whammy and some wound strings come back sharp - and then when you pull up on them (as when stretching strings) and release them in a snap, if they go back to pitch, it's an indication of nut bind. Sauce, dynaflow, bacon grease or motor oil notwithstanding, the slots may need attention.
(Also, I'm with the guys who put little or no wrap on the posts of locking tuners. The wrap is a great place for strings to stretch and flex if given the change, and if we can eliminate those coils of butt-biting trouble, I say do it.)
I know it's galling to spend up on a premium guitar with a vaunted reputation for general wonderfulness and then get less than perfection. And the strings may settle down, as others have suggested, after more break-in. But if not - and you're not comfortable putting tools to nut - you might consider paying a good tech to dress the nut. Might cost something, which I can understand your being annoyed to pay. But here's how I think of it: if it's a 300.00 guitar, and a professionally-dressed nut is all that stands between wall sculpture and a nice guitar, after I pay the tech 50.00, I still got a bargain, And if it's a 3,000.00 guitar, what's 50.00? I'm going to let that fraction of the spend stand between having a fancier hall hanging - or a great guitar?
Oh yeah, one other thing occurs. You probably know this, but if you have changed gauges - or gone to strings of the same gauge with different tension - you may have to adjust the tremolo screws in the back of the guitar to make the bridge float parallel to the top, as intended. You don't want the bridge pulled up at the front, or down at the back: when it's floating even, the pull of the strings and the springs are even, improving the likelihood that the system will return to that dynamic balance after whammification.
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* Tangent below: But I've had to dress quite a few - usually the 1, 2, or 3 - because they're deadening the string. The culprit is, I think, that sometimes the slots aren't properly angled down toward the headstock, and slightly toward the tuner for the string in question, so that instead of having a single unambiguous fulcrum at the front edge of the nut, the slot is morless level, so that the string is confused about where its break point is supposed to be. And the 1-2-3 grooves are generally tighter than I think they need to be.
