I hardly ever spin anymore because of my darn knee, so I’ve taken to doing Zumba classes instead. I do 1-2 classes/week and I notice my regular cross training/running Asics aren’t cutting it; I need more cushion and support with lateral movements.
I don’t want real dance shoes, as most of my Googling has led me to. Would volleyball shoes work well for all the lateral movements?
I was going to recommend dance shoes or going barefoot. I pole dance and have taken the Zumba classes at my studio. My pole instructor used to take the classes in pole shoes! I know, right? Doing Zumba in 7" hooker heels… I’d have never believed it if I hadn’t seen her do it. I’d never try it, but I didn’t want to be carting around three different pairs of shoes just to go to the studio, so I’d take my hooker heels for pole and just jump into the Zumba class barefoot. Because I do so much dancing, the callouses on my feet protect them quite nicely. I found I needed a bit of arch support toward the end of the hour and my Asics were just fine.
Having never worn volleyball shoes, i have no idea if they would solve your problem.
Good luck!
Barefoot! I like the idea but I have medium-high arches that usually hurt towards the end of Zumba as is 
Zumba in hooker heels just sounds painful. I still admire her though 
I find the hooker heels are designed for you to be on your feet for many hours (stripping, presumably, although on the pole, your feet aren’t on the floor all that much). They are surprisingly comfortable and far more comfortable than most of my regular 3" and 4" street heels. That said, I do not have the years of experience that my instructor does walking around on heels like that, so I can’t move fast enough in them to keep up with a Zumba class. She can, though.
Maybe think about those Vibram five-finger shoes? I don’t know if they offer sufficient arch support, but you might try on a pair to find out…
I use my regular New Balance tennis shoes. They give me great arch support while I’m moving around. They’re running shoes, if that helps.
My instructor wears dance sneakers, while I wear my standard Asics. I’ve definitely noticed that mine don’t offer the features which would be ideal for for Zumba - multi-directional support, a really light shoe, with minimal tread to help with sliding and spinning etc. I also suspect the split sole on my instructor’s shoe would make some of the ball of foot action easier; my sole is designed for running and just isn’t flexible enough. I don’t think barefoot would be the best recommendation; even dancers dancing ‘barefoot’ still strap their feet to offer support, traction and prevent burns.
Companies like Bloch and Nike make these sort of dance sneakers, although anything with a really flexible sole, and minimal traction underneath is probably going to serve you better than a standard sneaker. Or stripper heel. (Seriously? That’d have to see!)