Took it out to the garage and pulled out the old faithful expandable foam. Focused mainly on the shelf edges and just went back and forth to make sure that it didn't topple over the narrow edge. Left it out overnight and it set up. The shelf is pretty secure, at least enough to put on a couple of vials--though will have to lean more towards plastic ones. Still needs to be painted all over--maybe with a texture paint--and have some seashells glued on, but it looks pretty good. It's nice and tall, and takes up less space on the table.
Finished spray painting the shelf. Started with a thin layer of black, followed up by a gray texture. May have to go over it again, but for now it'll work.