The Inkbird IHC-230 can control temperature and humidity. I use it on my Cybercool thermo cooler.
Although I'm not sure if turning a compressor fridge on/off frequently is a good idea.
I have a cigar oasis excel with is good for up to 4 cubic feet according to the specs this fridge is 5 cubic feet according to its specs so maybe if it's in the basement it'll hold a steady temp and then I can still use beads and the active humidification? It'll be an experiment all the way around it sounds like
I'm not sure an Excel would do enough. I'd go for the Plus model if I were you.
I only use the beads to help the Oasis, they are all dry (meaning I never spritz them) save for a big bag down the bottom catching the condensation.
Really interested to see what you're going to do. It's possible to have it stable without tupperware - as it has worked before and people have done it.