Interested in the solution/outcome. I’ve dealt with the opposite problem, taming a inherently bright guitar.
Never thought about dealing with the opposite. Just some of my thoughts from anecdotal experience: bass frequencies can get really exasperated with gain. Not say the OP is using too much gain in a broad sense, but it there is a bloat in the bass freq’s gain in all the forms it comes in with a guitar rig, the initial elevated bass gets magnified to the point of unusable for normal purposes.
I gravitate towards dark/mids and introduce treble by rolling up the guitar tone knob, with max treble getting to a decent crunch tone. That being said, too much bass at the source (in this case sounds like it’s the guitar more than the PU), can be downright unusable l, especially in a full mix.
I don’t think changing PU’s is the quickest/easiest solution, because it sounds like the guitar is the source since you use the same pickups elsewhere. A high pass filter, which isn’t as prominent on a pedalboard as it is in the studio, would eliminate the problem easily. For the tones I like, I’d probably really dig the tone that resulted after the appropriate low end was cured with a high pass.