You said the two guitars are identical. Are they absolutely identical? Are you playing them exactly the same?
Big hands, low frets, small space between frets, not fretting in the right place, not having enough room to fret in the right place 'will' cause this issue. There's a 2 part fix but you may only need to implement one of them. Remedy 1: taller, narrower frets. Remedy 2: finger placement slightly farther back towards the nut (a problem if you have big fingers). You shouldn't have to push down any harder than normal but if there's not enough room or your fretting too far forward you will have trouble.
It's highly unlikely that 'all' the upper frets are not seated tightly.
The two guitars are exactly same model, they just have different pickups just. I'd say the guitar that plays properly has similar frets but not the exact same. They looks different profile to me.
Your suggestion of taller narrower frets:
the frets are jumbo so height isn't an issue, in fact I may actually prefer a little lower to feel more of the finger board beneath me as I've another axe (nearly the same as this guitar only it's a bolt on neck version) and it's frets are a bit lower and it feels a lot slicker and faster to play, where as the guitar with the problem feels like rail road sleepers for frets. The idea of narrower frets is something I have actually thought of because I don't have big hands, or sorry big/long fingers, I have short fingers and they are a bit chunky and to me it feels as though manoeuvrability is poor because the frets are too broad at the upper end, so Narrow frets at that end of the neck might be a good idea.
Although the guitar which is the exact same (bar the pickups), has these fat frets also and allows me to play the legato licks integral to my style of playing without this problem of applying silly amount of pressure.
Would narrower frets help that guitar too? Probably, although that is something I can put up with, however it's an improvement that might be worth doing some day.
I think the narrower frets will help the problem guitar, but I have to take it back to the luthier and see what he says. Surely he can copy the working guitar and do what he needs to do using that as a template? It's a really bizarre issue. The guitar hasn't been played a lot BTW, when I bought it, it was unplayed. I've only started playing it this year myself as I hadn't got around to modding it the way I wanted.