Could anyone tell me if such a thing exists and where I might go looking for one? The issue is that if we get a regular old 30" wide 34" depth 69" tall fridge and then build out the cabinet behind it is really going to box in the cooking area in our kitchen from the rest of the kitchen and in addition block all sorts of light.
If you have the ideal dimensions, try searching for European manufacturers of refrigerators who market here in the U.S. Traditionally, many European appliances will be smaller and more compact than their American counterparts, especially those appliances sold in England and the Scandinavian countries where living space is at a mega-premium. Perhaps you can get a better idea of what's available as far as depths go. Apartments in Southeast Asia (Japan, Korea) also have severe space limitations so check out what LG has in their line.