Well, in my book it's pretty straight forward: if it doesn't work... it doesn't work - and it's no use trying to force it!!!
We shouldn't waste our lives trying to make round pegs fit into square holes and if your S7320 and Jem don't put a big fat grin on your face when you play them, you should simply find something that does!
IMHO the all important "mojo" isn't as subjective and emotional as people tend to make it out to be... in my own experience "mojo" is more akin to baking a cake - even if we unaware of it. I think most people's "mojo" recipe is a little something like this:
2 ounces of features (bridge, no. of frets, PUs, scale length etc.)
3 table spoons of ergonomics (body shape, neck shape, weight, ballance, finish etc.)
4 pints of tone (bright, dark, defined, mellow, sustain, attack etc.)
1 3/4 mouthfull of aesthetics (we are all vain bastards!) and
1 pinch of emotional value (first guitar, gift from girlfriend etc.)
Obviously, these various aspects are decidedly intertwined and thus you need to find as good a compromise between the various qualities of an instrument as possible.
My idea with the cooking recipe, is that if one ingredience is off, the entire cake will begin to fall apart. I.e. even if the objective quality is there, our subjective preferences can make us not apreciate the culinary experience.
Luckily you already have a guitar that actually pushes the right buttons with you... Now all you need to do, is to figure out why and then find a guitar that improves upon what you already like about your GRX20 - sort of reverse engineering what works. Start by noting the main differences between the instrument that works for you (GRX20) and the ones that don't (S7 & Jem) eg.:
Features: Bridge vintage trem vs. double locking
Ergonomics: Neck shape round C-shape vs. flat D-shape
This is obviously just an example, and I might be totally off the mark in your case, but it's how I figure out what I like in an instrument... and even if it takes a while (and quite a few guitars) to figure out what works, the journey is a LOT of fun and the reward when you find something that really jangles your chain is simply grand.
Cheers and enjoy your quest!
"Do be do be do" - Frank Sinatra