Have you looked into how holding plates work? They use a container of antifreeze around the elements to retain temp and "buffer" it. You actually want to stop stuff freezing if possible, as there is a temperature spike when a liquid transitions to a solid (energy gets dumped out).
I think you could get everything you wanted with a fridge using holding plates, and some beefed-up insulation - "crystal kitty litter" is available very cheaply (at least in NZ) and is nothing more than re-branded Aerogel. A bit of that and some polyurethane foam to seal it, and you're set.