L-500XL, particularly with the filter (inductance control, allows it to alter mids at the guitar) is pretty impressively flexible. A great option.
If cleans aren't a primary focus, I'd have a good look at the PATB-2 (Parallel Axis Distortion), it's an absolute monster for metal, and has interesting cleans. It might have more mids and output than you want, though. Is the problem the JB's upper midrange, or is the guitar too middy?
For some samples of the PATB-2 check out
daemon barbeque -- he has a page full of just the guitar comparing PATB-2 vs SH6, too.
I'd avoid the Alternative 8, it's great for metal, but I don't think it's exactly an open pickup, or strong enough on cleans for use with a JC-120.
I've played my RG570 with JB into a JC-120 and loathed it, so I certainly understand where you're starting from, though I think my basswood makes the nasal honk issues even worse.
You might like the PATB-1, I got one a few months back and was very surprised by it. It's got funny hollow mids, though it's not lacking in mids overall, it's quite far from the totally scooped or notched out metal rhythm players mid-cut. Oddly both vintage and modern feeling. Not lacking in bass & lower mids, either, it's remarkably balanced in my guitar.
The PATB-1 (Original Parallel Axis) is like a Custom 5, only with sweeter harmonics and higher output without feeling compressed. The low string pull from the polepiece design is nice, as well.
I've found my PATB-1 to sound cleaner, a lot more open, brighter and yet less harsh than my JB. I like the JB... just not as a bridge pickup in this guitar.
I don't know how the Custom would work for cleans with a JC-120. It's a ceramic and bright, I've heard people get a broad range of tones out of it depending on the guitar, but I don't think I've heard an example of great cleans with a JC-120 and it... The Screamin' Demon might be a bit lacking in bass & push for heavier stuff.
Sorry if that meandered a bit, have a bit of a headache here, feel free to ask for clarification if you have any questions.