I have had quite a few jazzes and i liked them all! I don't get on with Ps though...
Try a few Squiers, from the Standards up to the VM et al. I've got a Standard and it's the nuts! I can get four or five really good, different sounds out of it. Really good slap sound too. Try rolling a little off the bridge pickup with the tone just nudging 30%, that's my usual fingerstyle setting for 80% of our stuff.
Dunno what everyone else is on about RE not getting classic Jazz sounds, all mine have done the job apart from my Warmoth which is a totally different beasty