Maybe there are solutions of this question like lowering the gain level on a virtual amplifier or something. Right off the bat I want to point out: doing that does not remove those problems, it just makes them more quiet while sacrificing the distortion level.
File to listen to is here:
So I recorded some DI parts and then put a software amplifier on the repeats of those. DI parts aren't played back perfectly (I tried though), but those should give you the idea of what I'm trying to play with distortion. Especially the first lick. I want to do a full scale run using that pattern, and every time I hit the note on 2nd string it gets killed by distortion. I tried using palm muting, but the problem remains and all brightness in the tone is lost (lick #2).
Double stops are destroyed every single time I play them, while using distortion (the worst happens when you play a second or a seventh). That's happening in lick #3. Palm muting is also applied there.
Lick #4 is a little sweep. Also get destroyed by distortion. Well, in 2nd sweep first note is kinda chewed, but I don't get the problem with the 1st sweep.
It happens on all pickups (I use a Gibson, so in all positions: Bridge, Bridge + Neck, Neck). I played using Bridge + Neck position for a more balanced tone. If I would have used Bridge – there also would be crackles in the audio. I really don't understand what's the problem about. If you need more info, I use a Gibson SG, compressor pedal and I play with a regular polycarbonate pick. There are no peaks or anything. Also somebody may advice to use a real amp – I don't own one.
I mean I'd also like to mention guitarists who have sweet distortion tones like John Petrucci, Mikael Åkerfeldt, Fredrik Åkesson or any other modern Progressive Rock, Progressive Metal/Djent, Metalcore band, but I think they all tend to use real amps. So I can't name known guitarists, who use software amps and pedals, so I'll just paste a YouTuber's solo moment that sounds sweet (still using a virtual amp).
Still not perfect if you listen closely, but not such crap as I get.