i would say if you are going to have a headache with a guitar and try to force it to do things it wasn't designed to do then don't do it.
from what you are talking about I would tryout a supersonic.
its got a stable strat trem.
2 humbuckers. more output. I never replaced the stock pickups, they sound great.
short scale glossy neck like the jag
plus they came off the same line as the MIJ jags of the day and used fender parts (the saddles are even stamped fender like on vintage ones)
try this out and see if you like it.
you could buy the jag, put in the 1/4 pounders and be completely happy with it like I am right now with my mustang.