So, I have an ibanez iceman ic400, it has a set neck, tune o matic style bridge, and medium frets.

I've recently noticed some problems with my intonation, I have the intonation set good when you just do a harmonic on the 12th fret, then fret the string to check if it's correct. But the problem I'm noticing, is that if I press down on any particular string (mostly the ead strings, but in some places the other strings) as light as I can, it'll be in good intonation, but if I press down as hard as I usually play, the note will get sharper, and if I press down the hardest I would realistically play, it goes more than a quarter step sharp.

I tend to use a heavier string set of strings, and try to have high string tension, so I use 52-10 sets of DR's. I also try to get a nice low action, but I have it set the lowest I can without having any fret buzz of any sort.

What the fuck is the deal here? I've been trying to just hold the strings lighter, but it's just not really my style for fast riffing. I might expect this sort of thing with real big frets, but I only have regular ass medium frets. I'm not sure if I should just switch to different strings or whatever.
I was considering just taking it to a pro if it's really something I can't figure out, but thats last resort, considering I know my guitar pretty well, and could probably fix this myself.