Hrm, you're right, those top pieces must just be covers of some kind. They have a short thread on them, about 3/16", which screws into that threaded hole on the top which you can see in the picture. The bottom caps have no slots in them. Although Maybe there's a setscrew on the inside face ... I'll check around for that.
I might have to disassemble it where it meets the body, but all those fasteners are frozen dead solid.
It is possible that the it's just a large diameter pin in a tight bushing, and it needs a lot of force to be pushed out ... just checking with the experts before I do anything rash.
Do you happen to know if there are complete parts diagrams for the 1939 LaSalle? I'll ask over in the general forum, too.
I have the Service Manual, which has a few diagrams, but if there's something that which has even more exploded diagrams, that would be very, very helpful.
Of course, this hinge was probably design by some guy are Superior coach works, who only machined a small handful of them. Oh well!