thick strings and tuning/intonation?

@OP Any chance the tuning peg is slightly giving in to the tension and mass of the thicker string? Something like that? Is it sitting in the nut/bridge properly etc
 
the hardware is top notch, so i doubt the tuning peg is the issue here.
you're probably onto something regarding the nut though. it's indeed not sitting as good as it does with e.g. .49 strings in D standard.

it's like this: i can get it in tune and intonate right for doing chords on the 1st fret upwards, but then the open string will be sharp. conversely, if i tune it flat to compensate for the open string being sharp, powerchords on the 1st fret upwards sound out of tune.

i really really have to be careful with my picking strength to avoid this. which strikes me as odd, as i can beat the shit out of my higher tuned guitars. gotta tune the lowest string sliiiiightly flat of course (like, 5 cents down) but it works fine.
it's obviously a technique issue too....fretted notes require a different picking technique than open strings, and i'm well aware of that.
 
13-62 strings in B standard on a 25.5" guitar would be too much for me I think, since you can go lighter with longer neck scales.
I really disliked 11-48 on my 25.5'' in Db standard, 10-46 works fine on that one. But on the 24.75'' I need thicker strings for the same feeling.
For stuff I record in B Standard with the 3rd guitar (25.1'' ) I have a 13-56 on and it felt great. Since they feel "straffer" when on longer scale a thinner low B might really solve your problem?
56 might be too light for you since you seem to prefer them much harder then me, but maybe something like 58 or 60 could do the job for you