I learned my lesson the hard way. I put in a mini fridge with the freezer plate as it appears you did. Nothing in the box, I froze water. Put 2 quarter barrels inside, and couldn’t get it below 40 and it was running 24/7. Because I’m picky, and like my beer cold, I had to do something. I busted out the fridge and ordered a mini freezer (well, it’s a fridge and a freezer, and goes from 0-40 degrees. Edgestar, I think)
Width was the same as the Haier fridge aside from a few shims, and I built a backer board and put 6 inches of propink on top. Box now holds 32 if I want it to, and that’s on the medium setting. Best thing is, it is not running 24/7.
Was definitely a pain in the ass to pull the fridge out and scrap it, but without an exposed coil fridge, I doubt you will get it as cold as you want with a full box.
Good luck!