Sorry to revive this thread but, and these may or not fix yours or other's issues, but I have a few pointers and comments to consider regarding this and other related issues that come to mind:
SM57
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You might not like the sound of an SM57. It has a particular sound that some people don't care for, but is still used in probably 90% of all recordings, profiles, cam IR's, etc. The positions of it can also affect the frequencies at which the natural "wind tunnel" frequencies are picked up, from white noise.
Some people will use a transformerless SM57, SM7b, or other MIC, that has a little less of the sm57's mid-range characteristics.
Thers will pull the mic back from the cab a bit, which drastically changes "wind tunnel" frequencies, which could be a good or bad thing. Some people will even remove a speaker grill to get the mic closer to the speaker. If an an engineeer has the cab in a different, live room but the amp in their control room, they'll have an assistant move the mic in the live room to sound the least "wind tunnel" (or phasey), and then readjust the amp or preamp/mixing board EQ's in the control room until the effect is minimized.
Tubescreamer Boost
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It's been mentioned that some high gain profiles don't have the problem. Some high gain amps are deigned to take care of the problem by design. I'm most cases with most amps though, most profiles are made with some kind of Tubescreamer baked into a profile or at least in the Kemper (or other modeler's) chain after the fact. This tightens up low end, and acts kind of like a gentle compressor and high pass filter, before the amp's gain stages. This helps get rid of rumble etc, and one can add a little bass on post EQ or amp EQ to help bring back some girth... Or just let it be so that the guitars play nice with bass guitars in a mix.
If one hates the mid-range sound of a Tubescreamer, one could play around with EQ and other techniques before the gain stage. If revamping or using an amp sim, one might even try the Andy Sneap technique on the DI, before the amp sim (you may have to use different settings).
Also, one could try a parametric EQ before making the profile, before the amp stage in the profile, or with an amp sim or whatever, or even a multiband compressor or even de-esser at the given problem frequency, to try to limit several issues. I'd Def start with the high pass and then a parametric EQ though, since compression etc will probably mostly take care of boominess rather than wind túnel noises.
Noise gate and other issues
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Many people have problems with their noise gates not being tight. No matter how they set the noise gate, it will suck too much tone or not clamp fast enough, so they opt not to use noise gates, because they cause more problems than they're worth.
The issue here is that hardly anyone ever realizes the reason for why noise gates suck for them... which is DECEPTIVELY simple as all hell to cure...
Make sure the string tree area above the nut and behind the bridge (as on a TOM bridge) are muted with some kind of fabric (felt, sock, hairbands) or whatever. The extra ringing from the excess string cause all sorts of crazy noise issues... Weird harmonics.. Noise.. Ghost notes.. Etc etc etc.. which are very difficult to pinpoint... I mean.. It could take you years or even a lifetime to figure it out.
Whatever the case, all these extra noise problems from the excess string can create a faux sustain that can not only cause the noise issues.. BUT THEY CAN KEEP YOUR NOISE GATE FROM OPERATING PROPERLY. Basically, the noise gate won't close immediate and will linger in an open state.. Causing one to crank the noise gate far beyond necessary, until ones guitar sounds like garbage. People might still not like a noise gate, but I'm pretty this takes care of the problem for most people.. at least partially, if not completely.
Sorry if these points don't fix the issues at hand, but I'm sure they'll help someone somewhere, who happens to have fallen on this thread.