Now THIS is a great idea! I have the same thing (converted old freezer to chest fridge with custom IoT temperature-controlled plug switch magic; though I now replaced it with a chest freezer that was actually designed with a thermostat allowing temperatures over 0 degrees celsius) and the same exact problem with the moisture accumulating at the bottom. The device actually has a hole to let the water out, but that's not helping as there must be a huge puddle of water before it even starts reaching the drain in one of the edges of the machine.
I might try that adsorbent trick, though I would imagine that I'd have to add some kind of grating on top of the adsorbent? Because I'd rather not want to place my water bottles into the adsorbent and have it stick to the bottom of the bottles.