While every factory produces a "clunker" sometimes, I'd be very surprised if your guitar was one of them. It does happen, but the attention to detail prior to leaving the factory at PRS is pretty stunning. Additionally, the care taken to shape, fret and attach the neck is bordering on the obbsessive.
Having the saddles all the way back strikes me as odd. Did it come from the dealer this way, or did you adjust these when you put on your new strings?
Let's start from the obvious and see if that helps. I would NOT adjust the truss rod at this point.
Are you dealing with the phase III locking tuners or the new vintage tuners?
If these are the locking tuners, are you using the lock or are you wrapping the strings around the post? If you have the locking tuners, then don't wrap around the post and see if this helps.
If these are the vintage tuners, how many wraps around the post are you using? Finding the right amount of slack to allow for two FULL turns around the post influences intonation stability on non-locking tuner guitars.
Are you hearing any "pings" as you adjust the tuning. A slight filing of the nut or some graphite in the nut slots might be helpful.
I know this is obvious and you may be rolling your eyes, but it's best to start at the beginning.