Before you change the pickup, I'd do two more things (you've already changed strings, and that's what I was going to suggest as a first) - try several picks and be careful how you pluck the string. I've spent a very fruitful hour on this looking precisely for nice Tele jazz tones. For the record: I've settled on Dunlop 2.0 mm gators, the grey/black ones. - following a great suggestion by Tim Lerch: if you're playing jazz on a Tele, it's a good idea to try and roll off a bit of VOLUME (say a quarter turn if the knob from full). It's the move that has found me my tone . Of course, your jazz tone will mostly be from the neck pup. But I also like the percussive sound you can get from the bridge PUP (I also roll of a bit of tone, but not too much).