Compact Refrigerator Thermostat Mount

I have a Kenmore 183.94679 (equiv 183.94673); the thermostat died and it wouldn't turn off the compressor (even when set to off) - everything froze. While Sears is very good about selling replacement parts (http://www.searspartsdirect.com/model-number/18/394673/0582/0163200.html), the thermostat (Parts #: RF-7350-124) is no longer available. Someone else had had this problem and talked with Haier to find out the RF-7350-101 would work. However, when I received it, it wouldn't mount to the fri