This is the one that I use: https://www.amazon.com/Vicks-Filter-Free-Ultrasonic-Humidifier-Moisturized/dp/B00F8MJXMG
It has a decent capacity so I'm not constantly refilling it. I use it in conjunction with this controller: https://www.amazon.com/Inkbird-IHC-200/dp/B089K8J81Q
Yeah it's a bit surprising that it's being used up that fast, especially in an enclosed environment... the fridge is well-sealed, right?
My 1.2 gal humidifier in a 24 cubic ft stand up freezer only needs refilling every week or so, and that's with a 4" hole and a fan going on for 15 minutes every other 30 minutes. But, my chamber is in the 55 degree basement, so it literally never cycles on (therefor, humidity isn't as quickly removed). Plus it is pretty full of meat, so that will help.
And now that I type that out, I wonder if that's your main problem, the fridge isn't full enough. When it has a lot of product, the volume of plain air is much lower, and the drying meat adds to the humidity. So the humidifier doesn't have to work as hard. But not in your case.
Regardless, I'd upgrade the humidifier, to something like this Vicks one I currently use with 1.2 gal capacity or this Crane one that I used to have (which worked fine, just wanted something a little bigger), or this huge unit from Honeywell which might actually be too big. Remember it MUST have a switch or a dial, because it needs to come back on when the power switches back on. Push button controls tend not to do that.
I use this: https://www.amazon.com/Vicks-Filter-Free-Ultrasonic-Humidifier-Moisturized/dp/B00F8MJXMG/
In my stand up freezer. It works great but it's too big for me. It takes up a lot of height so I lose some room on one side. Not the biggest deal in the world but if I was buying again I'd look for one half the size and add water to it more often. It has the dial so when my inkbird tells it to kick on, it kicks on.
Hey, I have those inkbird controllers. They're pretty good. Couple of things tho:
Kinda hard to explain, but you have to use appliances with physical on/off switches. Otherwise it won't work cuz the controller kills power to that appliance, and if you have to push an "on" button, like this one, after it receives power, then it won't work as intended.
Check out a swamp cooler, or evaporative air conditioner. Uses water to cool. You gotta fill it, but if you're handy, you can run a RO water line with a float valve to self fill. It's gotta be an open basin, or top fill to do this tho. Otherwise, it'll leak all over. The one linked has a continuous fill already set up. It also has physical on/off.