On the basis of teaching a man (or woman) to fish so they can fish for themselves next time around, this is what happens when one types 'shallow depth fridge' into Google or another search engine - this sort of link appears appears.
http://www.diybanter....ow-depth-fridges.html
The link is rather old, but some manufacturers and/or Comet as a potential supplier may still be relevant. Futher down the text, someone suggested that fridges designed for use in caravans may do the trick, though there is probably a price-premium on such animals.