Many boats, like the flat floored bass boats have coolers that sit flush inside them. I have never seen an electric one to be a real fridge, but you may look down that path.
That's actually a brilliant idea Keith!
Steve... check this out... recessed storage -
http://forum.ih8mud.com/80-series-tech/167864-more-cargo-room.html
Where is your spare going to end up? I don't know if a 35" tire will fit in the stock location, but if not you could put the spare on a swing-out tire carrier and free up the spot where the factory spare was.
My
Edgestar measures under 21" tall, if you have 12" of space to work with, then your recess would only need to be 9" deep. That's not a whole lot, to the point that it would detract from departure angle. Of course you would have to beef up the 'storage' compartment to hold up to a heavy, loaded freezer-fridge and build a heavy-duty skidplate for it. The job would require quite a bit of fab work and engineering, but I bet you're capable.
You could build a hinge on your sleeping platform to access the fridge down below and fit a full size fridge in the very back, sitting nice and low. The fridge needs to have some ventilation of course and proper tie downs, easy enough though.