I think it looks like it was done by a coachbuilder that normally made hearses, not a Chrysler factory prototype. In one of the old pics on the page that @Jonas linked to above, you can see that it had 2 rows of seats, so the back would be too short to fit a coffin though.
The roof slopes up, following the lines of the fins. The rear pillars are made of curved glass. These are the kind of things you'd expect to see in a 50's hearse conversion, so it's easier to see the coffin inside. Also, I wouldn't be surprised to discover that the tailgate opens like this: