This was for me the greatest challenge in getting good sounds from medium- to high-gain presets in the Axe-Fx. Different firmware revisions have had the syndrome to different degrees, but it has pretty much always been there in the amp sims I use. There are several things you can change that will help you tame them. First, it appears to me that the undesirable overtones originate primarily in the power amp section of the amp block. Beyond the obvious steps of turning down treble and/or presence, some combination of the following changes has always worked for me, in rough order of preference:
1. Reduce MV and increase Drive.
2. Reduce Hi Freq Resonance.
3. Reduce the Hi Cut frequency.
4. Increase Sag.
5. Reduce Transformer Hi Freq.
6. Place a PEQ in front of the amp block, set filter 5 to Blocking, and turn down the frequency until the sound just cleans up.
You're walking a fine line here, so make small changes to one parameter at a time and listen carefully before going further. It's easy to get rid of the harshness at the expense of dulling the edge of your sound.
Also, work with the amp sim first (Drive block bypassed). Once you've got it cleaned up, kick in the Drive. If the harshness returns, tweak the tone controls of the Drive block to get rid of it.