Despite having a copy tucked away somewhere, I hadn't ever twigged that It Hurt's So Good was a Millie Jackson hit. Here's a nice little evolution of the song from the original:
through the Millie Jackson hit:
and on to the version we all love:
I'd stick the Genzler Magellan on your list. I had and lived the smaller version (sold due to lockdown, but top of my list once gigging again) and your budget will cover the 800w version. Will be great with all the styles you mentioned.
A different approach is to get the lead guitarist to tailor his soloing ( caveat, there will be some bits that will need to be played note for note) to take up some of the slack.