One last question: Do you detect this same unbalanced slap stroke volume when playing only acoustically (no amp)? If yes, it's probably a string or string setup related issue. If not, it's more likely a pickup / amp setup related issue.
While the fingerboard pickup is probably your primary concern, you'll probably find that your bridge wing pickup does pick up a fair amount of slap. After testing it on my double bass, I could probably have just gotten a bridge wing pickup; at least the Vic's Model B single wing pickup is sensitive enough to also pick up slap. But I wanted more balancing control and that only comes with both the wing and the fingerboard pickups and a 2 channel pre-amp...
All that said, on my bass the wing pickup was way too boomy on the bass side, so I moved it to the treble side of the bridge. A number of folks here have found the same thing with Vic's as well as a number of wing pickups from other companies. I have a Deuce1 bridge so making that move to test it was pretty simple, and it proved out to be better on the treble side.
I have to wonder if that same change might improve your slap balance, since the bridge pickup does also pick up slap.
Regarding the strings, I ran the "medium" tension D (.105") and G (.095") of the Dirty Guts for a number of years and really liked them. At first I ran them with the highest tension E (.170") and A (.155") but I didn't like the gauge match, so then I moved to Innovation SilverSlaps E and A. That combination worked well for me for about 5 years, by which time I was ready to move to a more old-school plain-gut sound. I wanted to have a full set of plain guts except for the cost, but as an interim change decided to try out for the frist time the fattest and highest tension full set (.170", .155", .130", .105") of the Dirty Guts. I have been extremely happy with this fat highest tension Dirty Guts complete set and will probably stay with them on into the future...
As mentioned this fattest and highest tension Dirty Guts set is dark with noticeably increasing decay from G to E. The gauges are well balanced., and very close to the gauge of the plain gut strings that I had thought about getting (Lenzner). Like the lighter tension Dirty Guts they move a lot of air. They are also noticeably higher tension, probably a little higher tension than the SilverSlaps that I had been using. At least on my bass, for my playing, they are excellent for pizz, arco and slap. (I did have to open my bridge and nut slots slightly, and my fingerboard was already dressed for thick strings.)
But... Everyone's double bass is different, and everyone's sound goals and playing touch are different. If I were in your situation I'd probably try the bridge wing change first. If that didn't help I'd consider some experimenting with the fingerboard pickup location. And if that didn't help I'd consider string changes -- if you prefer a more modern tone, you might want to try Innovation SilverSlaps/Golden Slaps or similar wound synthetics from other companies. Some people are even using Spirocore Solo gauge for slapping.
Gollihur Music's Strings section (NFI) is amazing for learning about string options.
I wish you the best as you work out your situation!