I presume you are using round wound strings to tear up your fingers like that. I played flats on my '65 Jazz in the 60's and then switched to the Fender Black Tape Wound strings in the early 70's. Then my '65 Jazz was stolen along with all my touring gear and I didn't find a good replacement for it until 1985. That replacement came with Dean Markley Blue Steel strings already mounted. I had used Dean Markley Blue Steel and DR Black Beauty strings since 1985 when I got my '82 Jazz until 6-years ago when I got the LaBella Tapes.
Flats may not have the zing you're looking for but the LaBella Tape Wound strings might work great for you. They are super smooth and slippery and are not going to kill your fingers. The White tapes are the brightest sounding of their offerings and the black tapes are the darkest sounding. They also have white over a gold core and white over a copper core, which are somewhere in between the white and black in sound. I chose to put White Tapes on my Passive Jazz Bass and love them. By the way the white tapes are semi-opaque and you can discern the color of the cores through them. The white tapes have a Nickel/Steel-color core.
A real plus on these LaBella tape wound strings is the balance of sound from string to string. With all the round wounds I've used, I typically would play the higher E on the 7th fret of the A string instead of the 2nd fret of the D string because the E on that second fret always sounded kind of weak and thin. Same with the A on the 7th fret of the D string instead of the 2nd fret of the G string. With the LaBella tape wounds the sound of those notes in both places is so similar I just play them at whichever location is closest to what I'm already playing. The notes on the 2nd fret of the D and G strings have plenty of body. They are by far the best balanced sound string to string I've ever found.
