Couple of pics will help...
I would not go overboard on string / pole piece alignment.
https://amzn.eu/d/gav3eTY
String to fretboard edge is more important.
Might be more down to the DD Pup, or 60's v 70's Spacing if rear pickup. Any room to move the pup side to side - pup mounting (or route)
I always thought the P and J had same bridge and spacing.
Have a good look at the barrels, the intonation screw hole and the string groove - maybe a slight difference, and you could swap the order?
I much prefer the F HMB over the LQ, looks sleeker.
Get some pics up.