For me 2300 Hz is the magic frequency to cut for harshness. The trick is to set your Q to 10 and boost a random frequency maybe 6-9dB while playing a loop recording of the horrible pick attack. Then sweep as
@Ocnor suggests. You’ll eventually hear when it gets really out of control obnoxious; that’s your offending frequency. Then cut just enough to get rid of it without taking away too much character. I found that for me the worst of it began at 2284 Hz and ended at 2321 Hz, so I split the difference and cut at 2300 Hz. If you need to, you can also widen the Q by lowering the Q value, and that will help further with the taming.
The input EQ of the amp block is awesome, but you have to reset that frequency cut every time you switch models, so you may just want to use a Filter Block right after the Input Block instead, maybe using the Notch Filter. I've done that before, actually setting a maximum cut of 20 dB at Q 10. It's way too much, but the idea with this approach is then you can boost the mids in your amp safely without driving an icepick through your eardrum, no matter what amp or IR you choose.
I've also found that just trying IRs you never touch (possibly with amps you don't usually try) can mitigate it. I was thinking that my current harsh pickup (Schecter Sunset Strip), much like the JB, must sound right to the designer, and there's got to be a context in which it can work okay and deliver a cool tone. I finally found that for me just trying some IRs and annoys that were out of my wheelhouse really took care of it. For my other guitar though, a pickup swap (from JB/59 to Saturday Night Specials) not only cured the harshness completely, but utterly gave the guitar endless dimension too.
Lastly, changing the value of your pots can possibly mitigate the problem. On my other guitar I first tried swapping out the two 500k pots on the bridge to 250k, and that really did the trick. Afterward, I still didn't think the JB had any versatility, and that's why I went for different pickups in the end. But for taming the harshness alone, the changing of pot values totally took care of it. Alternatively one can change pot value by installing a resistor, though supposedly the taper changes.
I do feel your pain, so Best of luck to you!