I agree with Reverseapche that a hinged top (hinged at the rear) would be the easiest and best way to go. With one complication.
The easy part should be getting the top free of the base. The top looks to be pop riveted to the rim of the walls. Drill out/punch out the pop rivets and the top should lift off. But don’t lift it off much yet.
The complication is that the cooling unit (the evaporator) appears to be attached to underside of the top. There should be a small copper tube (I think visible in one of your photos) coming from the condenser to the evaporator and a larger copper tube going from the evaporator to the inlet of the compressor. These copper tubes can be bent around a couple of times but not flexed repeatedly. I’m guessing that the compressor and condenser are underneath the fridge with the tubes running inside the back wall. It could be that the condenser is on the outside of the back (no photo).
So…once the top is free of the sides, carefully lift the front of the top and prop it up on an angle such that you can get to the fasteners that are holding the cooling unit to the top. When free, use a stool or temporary framework to support the cooling unit in roughly its original position and lift off the top.
Now you will want to permanently mount the cooling unit. The best place would be on the back wall of the interior near the top. If the tubing or whatever won’t let you do that, then get a couple of large right-angle shelf brackets from the hardware store, attach them to the back wall and hang or support the cooling unit in roughly its original position. Be sure to drill for attachment to the back wall away from where the tubing looks to run.
Now you should be able to put the top back on with hinges at the back. Standard door hinges should do the job. Some weather stripping might help to seal it.
I know it sounds difficult but you can do it. And those things are cool. Make a fermentation chamber of one and a kick-ass kegerator out of the other! Cheers.
Please feel free to email me with further question/conversation/photos about this project.