Looking for "brighter" sounding flats.

For this particular bass, here are the specs (second from left in the photo):

Franken-P Bass.
Maple/Maple Board Jazz neck
Fender 'Original '62' pickup.
Swamp ash body.

I've tended to keep flats on here but overall, with the current setup, most flats I've tried sound way too muddy. I'm sure it's a lot to do with the pickup, which I'd rather not change because I like the overall voice of it. I've tried standard LaBella flats, Dunlop Chromes, Ernie Ball Slinky Flatwounds, maybe one or two others, but not as balanced overall in tone that I'd like. I have half-rounds on my Jazz which I like but they sound wrong on this bass.

If there are any others you'd recommend I try, please let me know. Mostly these have been in the 45-105 region, but I'm happy to go to different gauges for this trial. Thanks for your help!

 

I actually have TI flats on my Squier VT Fretless Jazz where they sound brilliant. I initially bought them for the P but again, didn't much like them. My gut is telling me the pickup will need to be swapped, but I hate to do it as in general I like it's response very much.

 

Already tried these, but thank you!

 

And that's the thing - this bass is heavily gigged. Dropping about $80 per set might end up killing whatever profit I make from playing!

 

Are the Cobalts much different from the Slinky flats? Pleading ignorance as I've little experience with EB strings. I've tried the Slinky's (in fact, that's the set currently on the bass).

 

I have TI flats on my fretless Squier Jazz - love them on that bass. I tried them briefly on the P - didn't like the way the pickup translated them.

 

You know, in seeing all these responses, I'm starting to wonder if maybe finding a warmer sounding roundwound would be a consideration. As much as I love the feel and playability of flats, ultimately I need to have a useful sound for multiple gigs. Any thoughts on that?