So the glue seemed to hold, I re-assembled the puzzle and lubed it a bit, and it moved pretty well. I put it up on the shelf, and a few minutes later...
...Pop, it exploded into pieces again.
I'll re-build it again, perhaps if I can find some weaker springs, but I think I've hit the limit of 20 year old plastic durability.
To further compound my failure with this particular mechanism, I decided to clean my zodiac ball (same mechanism), now that I know the internal workings.
It was a bear to get apart, but once I did I figured I'd clean it up, reassemble and lube it. It barely moved before, so I figured, how much worse can it turn?
Now I can't reassemble it. Either it was already breaking, or the stress of getting it apart caused the plastic to fail.
Word to the wise: If you have one of these puzzles, leave it on the shelf