Thx for all your replies! I played it some more and I love it's jangly and gritty tone and the overall feel.
I know about all the trouble people seem to have with the stock Jaguar bridge and it's surely very prone to buzzing because of the way it's constructed. Mustang bridge saddles are heavier (solid copper) and have a single deeper string groove so they tend to work better. However a lot of this bad rep also comes from people using thin strings on Jazzmasters and Jags, even Fender puts 009 or 010 strings on the reissues which is way too thin.
The stock bridge works fine with 011-049s after some TLC. I took it apart completely and reassembled it, putting the three different length springs where they are supposed to be and locking the saddles by choosing the right angle/screw length. No buzzes, no string skipping etc. 8) As my goal is to keep this Jag as stock as possible I'll try the original bridge first.
The stock PU's are just great so no BKP's needed here. Should a pickup short out or fades away I'll have Tim restore it.