As shown above, PRS Guitars have a built in compensation for sounding sharp, especially in position 1.
If you are having a problem with other fretted notes further down the neck sounding sharp, and if your guitar is properly setup and intonated, you are probably fretting too hard. It is true that heavier strings will help you with this problem, but only for the length of time it takes for you to build more finger strength to compensate.
Examine your technique. Fret hard enough to get clean tones, but not so hard as to depress the strings into the well between the frets.
Fret height can help or hurt you here. Shorter frets are your friend if you grip like a gorilla and you'd definitely want to stay away from jumbo frets and/or scooped fretboards (like Malmstein uses). But with shorter frets you loose some access to some techniques like pressure bends and pressure vibrato.. It's all a trade-off.
Your technique of tuning a bit flat will have the effect of making all open string tones flat while your fretted tones are 'sounding right.'
I suggest tuning concert pitches and adjusting your technique...