Isn't there an amp out there that allows MIDI control, and saving of settings?
This was a huge reason why I went with an ADA MP-1 back in the 90's- I could never understand how people played live without changing their amp settings, at least somewhat, to play covers. I mean, I get the whole, "use different guitars" thing, but for me, having a programmable, MIDI-switchable amp that I can set up with various tones was just what I wanted. I stayed with that same setup for the next 2 decades.
Then, for the same reason, I had always truly wanted a Tri Axis, and I found a fantastic deal on one, so I bought it. Programmable, MIDI-selectable amp settings. But since I got an Axe III shortly thereafter, I really haven't used it much. But if I were ever to gig again, I think I'd want to at least try it in 4CM with the Axe.
I'm not suggesting the answer for you is to go out and buy some 30 year-old rack gear, but the principle of using a real amp that has programmable/switchable presets..., doesn't that still exist?
Heck, try out these NDSP plugins that are on sale, get a workhorse laptop and set up some type of MIDI switcher, and go really crazy with 21st-century digital guitar tech, and use that live!