But if I put things on top of it, now I can't get at the food.

I mean, I have one of these as a meat freezer, and sometimes I put things on top of it, and then my wife gets mad at me and moves that thing somewhere because otherwise nobody can open it.

Things on top of my vertical fridge on the other hand (my cat for example), can stay there indefinitely.

Wouldn't a solution be to have the opening on the side and pull it toward you, like a "box on wheels"? As long as the sides of the "box" are thermally insulated, it seems like a sound solution for the stated problem (but certainly not one that's mechanically the cheapest/simplest).