I guess I am having a problem trying to visualize your portable cooler install. It appears to be mounted on a slide maybe sitting inside the bottom storage area. the only fridge units I have run across are the small one sitting inside the POPUP trailers or large up-right home type fridges in the larger trailers.
Can you give us a model number of the unit. I assume this works on AC and DC perhaps... I am guessing this on the order of a house ice chest.
Something like this?
I have on occasion brought along a second desk height dorm room type fridge sitting on my outside front deck to get more cooling area when camping. It just clears my pull-out tent bed on my off-road popup.
Having available ICE is one of our biggest problems camping off the power grid.
Roy Ken