For the solutions that have been offered, I'm not certain we're either talking about the same thing, or hearing the same thing.
From the YT clips that Governator and I posted, we're talking about that "woomm woomm", for lack of a better way to describe it in words, that happens immediately after the palm-muted note is picked, that does not exist when JP does those "chuck chuck" palm mutes, that he even mentions are totally choked off. I'm hoping we're first in agreement that that's the issue of focus. I don't think you don't have to run the real amp so loud that it requires an attenuator, and mike it up and use a certain IR to get that choked-off sound. The amp simply reacts that way.
So it seems to me it should also be attainable in the Axe, just in the amp block, without needing a certain IR to make it go away.
I believe, and I could be wrong, that no amount of adjustments afterwards, can remove that rubber band-sounding, after-note 'flub', nor should be necessary. I think it may have something to do with the way the amp is modeled. I've had this concern for a while myself, but chose to work around it by using different amps, since I can't seem to get rid of it. I've tried reducing the bass extremely low, then making it up in the GEQ, as has been suggested, but that doesn't eliminate it, and then the overall tone loses its full bottom.
If it turns out that I end up using a certain block in a certain way, that's after the amp (or maybe even before, although a real JP2C doesn't need a drive pedal to give it that tight, crunch tone, imo), that gets rid of that lingering sound, then I will have learned something valuable, and appreciate it, but it will probably still seem to me like, for example, trying to fix a particularly mid-range, 'honky'-sounding pickup by EQ'ing out those frequencies, rather than replacing it with a better-suited PU.