Now days (since I discovered the TBird and SG) I'm in the exact same boat. A single coil P and a split coil P both have a sound I like (I still like a TBird or SG Humbucker better) but a Jazz pup near the bridge (with the exception the of a Warwick Thumb bass) is just not my cup of tea.
I have a SS Squire Jag as well and modded it with a custom built John East three stacked knob active preamp (Vol/Pan, neck bass/treb/brite, bridge bass/treb/brite) to see if I could warm up to the Jazz pup on that bass, but still no luck. The good news is, the split P on the Jag is quite nice so I pretty much leave it fully panned to the neck. I've thought about taking it back to passive and installing some Geezer pups in it, but I hate to mess with that sweet sounding stock split P.