I’d try new saddles. GraphTech makes some 3 barrel TUSQ saddles that would also sound really good with a jazz rig. I use them on my tele and play mostly rock and blues. If you can’t get close enough intonation with another set of compensated saddles, try a 6 saddle bridge. I dabble in jazz chords and they sounded sour at certain neck positions until I swapped to the compensated saddles.