Before you go swapping pickups - have you played around with the EQ on your bass? I went through a similar thing with my ATK until I realized how much tone shaping I have at the bass. I roll treble off nearly completely, boost the lows a bit and boost the mids a bit more than that. The result is a tone that's much closer to a vintage passive-pickup sound. Maybe you already did that, but I thought it was worth mentioning.
I have, but I was going to wait until I received my Dually and sufficiently played around with the EQ once again to make up my mind on swapping them or not. Thanks for posting what works for you, I'll have to give it a shot. Do you find yourself having the guitar volume relatively low? The better tones I've gotten thus far have been with the volume on the bass itself only around 3 or 4, tops.
If that's your only bass, might consider getting an cheap passive backup. Just random idea
I'd be lying if I said I hadn't thought about it. I have a friend with a old school ripoff Fender from the lawsuit era w/ passives, maybe I'll try hitting him up.
I dig the Swollen Pickle a lot on bass. Have you messed with the internal trimmers?
Oh yeah, I absolutely love that pedal. My go-to setting right now is very aggressive while still retaining a lot of fat low end. I like it to roar. It takes a ton of tinkering with that pedal, but the versatility is amazing. I always enjoyed the tinkering, myself.

