New CE owner - bridge question

Sorry to bring the subject back to guitars again, but needs must.

I've changed the bridge setup so that the tremolo is floating rather than decked. 12th fret intonation is good.

BUT when I fret hard pretty much anywhere on the neck, the note is going sharp.

So.... Do I need to change the intonation to allow for fretting hard?

Or - have I inadvertently set the action too high, and I'm bending the strings out of tune when I fret them?

I didn't have the 1.5mm pick that John Mann uses in his video to set the spring tension, so I set the bridge parallel to the body by eye.

I suspect if the action *is* too high though, it's because I've set the bridge screws too high. I was using what I thought was a 2.5mm hex key, but it wasn't marked so maybe it was slightly off (e.g. imperial not metric), or maybe the PRS bridge needs a lower setting than his replacement bridge?

Any thoughts on whether it is the action that's throwing it out, and if so, how to fix it, would be much appreciated.

Many thanks JP..
It could be the action, or you could just be squeezing too tight. You can lower the action a little to see if it helps (seems like it should), but a lighter grip can help as well. FWIW, even on my lowest action PRSi, regardless of bridge, I can squeeze tight and pull the note out of tune a little.
That's usually a matter of fret height. About 15 or so years ago, I was playing a 12 string acoustic regularly, so my grip had intensified a bit. I bought a guitar with jumbo frets on a Sunday, brought it to rehearsal Monday, and returned it on Tuesday. The frets were just too high for the amount of pressure I was using. Took a lot of effort to loosen my grip over the years, but I still tend to avoid the jumbo or higher fretted guitars.