Use the pull fat and or the pull presence on channel 2 and or assign the EQ to channel 2. Dont know what you already tried though.
I was afraid that I would have to set the EQ to Channel 2 if I wanted to get a good tone out of it.
I have it pretty much EQ'd for the most Fendery ( I know it's not a Fender, but it came from one) Clean with just a little bit of breakup.
I might settle for a Jazzy Clean tone for Channel 2.
As for the JJ's, they sound great in, Fender, Marshall & Mesa amps but sounded like mud in my Soldano. Believe it or not, the Sovteks & Electo-Harmonix sounded best in the Soldano. I think that the Sovteks & EH's are too harsh for the Mark IV, but the stock Mesa tubes sound really good in my Rectoverb.
I think that every amp, or type of amp, has it's preference of tube.
I'm not sure if it's the JJ's or just the fact that there are no more Sovteks in my Mark IV, but the tone is much more robust and the Feel is incredibly touch sensitive.
It all comes down to what type of cabinet, guitar, settings, style, etc., you are using. What is the so-called "Holy-Grail" for me might not even sound good to you. Most Bass players will tell you that most of their tone comes from their fingers. They seem to experiment more with guitars, pickups & strings than amps, and are usually drunk (aren't all Bass players drunk), but I think that the statement is fairly true.
I've seen great guitarists use a Peavey Backstage Plus & an old Les Paul or PRS and get the most incredible tones out of the setup. They hand the guitar to me, and the tone is instantly sucked into the vortex.