[FrankHudson]

I was going to recommend the Fender Mustang amp, which does a reasonable Blackface sound and can do it at any volume level, but I read right you want the amp to double as an acoustic amp AND you already have a full-range PA speaker (the Mustang can take an acoustic with a clean setting and work that way, but it's not a full-range PA, though depending on needs, it might be good enough). I'm even guessing the PA speaker may carry your vocals in your practices, so it has to come along anyway. Did I get that right? One of the nice things about the Mustang is that once you have your presets all loaded up, you can just use the optional footpedals without need of a tablet or computer.

Even simpler is the Fender SuperChamp XD. Again nice lower volume blackface sounds, small and light to carry, and very simple to use without a computer. Not a full range PA either, but a cleaner blackface patch doesn't sound bad with an acoustic.

So I think your idea of using a smaller modeling pedal in front of the PA for the electric guitar in front of the PA may be the simple solution. I've never used them, but some folks like the SanAmp fly rig pedals, which have a smallish footprint, but none of them include a wah that I know of. There are still other choices in small footprint "Multieffects pedals" that include a wah treddle. Auditioning that class of thing at a store might find your solution.

The battery in your Variax should carry you through any gig if remember to charge it, and it doesn't drain (except for the tiny discharge it would get even sitting on a shelf over time) unless you are using the Variax pickup.