It is all about the watts for the 12v element. At 100w it does not cool down the fridge, but at 200w it does. The 120v element was pulling 300w, so it works great.
EDIT--to be more accurate, those 100w and 200w measurements were not at the element but were what the converter was pulling according to the Kill-A-Watt. Jack up the converter's adjustable voltage and get more watts.
Getting enough voltage out from the 12v element's board terminals is the problem, with all the voltage drop in the board, from chassis connection block to the board, and from the battery to the chassis block.
I have 14.7v out to the element, but the thin pos wire out from the board to the fuse and on to the element is very warm/hot. Some wasted power there, but needs to connect to the board terminal so can't go big on the wire really.