It’s really wild to me that your bass is as bright as you say: I have a Talman TMB605, which has the same pickups (albeit in standard P formation) with GHS pressurewounds and the tone is huge and deep. Like, notably so. I wonder if it’s your strings.
Also, just be aware: in my house, which is an extremely old 60 cycle hum factory, the bridge pickup is basically unusable. It was a shock when I first took that bass to a rehearsal space and I was able to blend in the bridge pickup and it didn’t sound like we were playing next to a large waterfall. Just keep that in mind if you play a gig somewhere with old, poorly shielded electrics.