I think the ability to get cold would depend on how much ammonia had leaked out. On the other hand, I've never smelled ammonia that was "super sweet". I have smelled things when left too long that did leave a "sweet" smell.
It sounds like you are using this daily...are you? That will make the fix a little more complicated if you are. What have you used to clean it? Is there something in the fridge that has sat too long that has maybe been overlooked? It sounds like there is, or has been, something in the fridge that left a smell that accumulates overnight then you get a good whiff in the morning.
I would scrub the fridge, and freezer, down with some hot water and Dawn; rinse it out then place a large box of baking soda for refrigerators in the top and bottom. You might even place an open container of 4 or 5 charcoal briquettes in those areas as well and leave them for a few days. At that time remove them and check it out. We leave a box of soda in the fridge and freezer 24hrs a day.
Danny & Susan wife of 53 years
2019 Ram 3500 Laramie CC SB 6.4 4x4 4.10
2020 Montana High Country 331RL