I'm looking for a bridge humbucker with a Tube Screamer style mid-hump. What company and humbucker would you recommend?
Blues rock, jazz, jump blues, alternative county, outlaw country, county blues, & Texas blues.
I'm not sure the JB is what I'd recommend for that style of music. I suspect it's hotter than what the OP wants and I agree that the pickup has bass. It also has a high mid punch to it, which is great with the right guitar, and IMO really wrong with the wrong guitar.
I'll ask the standard question here: what kind of guitar are we talking about? What wood? What bridge?
If you like the TS sculpting of the sound, why run the guitar through the TS to get that sound?
I want to mentioned something about Rio Grande pickups here because I recall liking them, but I can't link up what I've actually played with what's on their website. They had some nice mid-punchy, bluesy pickups that I got in a guitar once, but I pulled them as I'm not a blues player. They were great....just wrong for my application.