It's been a week with this thing and no matter what I do sounds thin, lifeless, and fake. So frustrating.
I was in the same place just a few weeks ago. It took a lot longer than anticipated to get results that don't sound like you describe, I'm literally just this week getting over the '90% there' barrier. That last 10% is a b*tch.
Problem is we're all so different in terms of expectation and playing style its difficult to get a recommendation on what to tweak. I'll offer my solution but I can't guarantee it'll work for you.
First revelation was to use the tone controls and drive/master to set the amp feel, then the GEQ to set the 'tone' (with lots of toing and froing between). You need a lot less top end than you think, plus your ears get accustomed to the tone and fatigue can cause you to bias the EQ too bright or too dark. Having a reference track to refer to helps.
Second was discovering that Preamp Bias, Definition and Harmonics were the key to getting the pick attack feel and distortion quality right. Most amps feel 'clacky' to me with too much pick noise and 'thwack' on leads, reducing the definition (-2 to -4 usually) helped.
Bright switch Cap value, mess with it. Really has an important effect. Ditto the Power Amp MV Cap (I set it to 30-50pF on amps such as the Dizzy then reduce the top end with EQ with good results)
I'd say I'm now at about 94%, still work to do but there's light at the end of the tunnel now. With Q7 I expect things will improve a lot too.
(Note, there are no rules, I use the poweramp modelling with a tube amp as well as with a SS, turning off the PA modelling is one way to work it, but not the only way).