1st this: "The thing is, I've already got an American Jazz that's survived the purchase (and sale) of every other bass I've ever owned
then this: "I am very partial to Fender and even more partial to jazz basses
....so......I think you should not get another Fender Jazz, seems like you have that category locked down......you will either not like the new one after a while or really like it and be tempted to sell the original (not likely from the 1st statement, and you'd really regret it if you did)....but then you would have 2 Jazzes with (possibly) not much difference between the 2, and not really playing one of them much ...I think you need to look at mid to high end stuff.... Ricky's, Ibby's, Yammys, Gibby's, Hoffy's ?, even Epi's, Squier-ee's...
.....problem is you sold every other bass you had so: .hmmmmmmmm......I guess play them, borrow, rent etc and you may find something......great hobby IMHO.....tell Granny that her purchase may or may not be permanent
.....that rig sounds awesome, but you'll spend forever trying to find something better or different enough to keep you happy....
YMMV