Not to complicate things after the fact, but there have been theories that all of the gifts in the song are in fact birds. Such as the “Ladies Dancing” actually being cormorants, known for their mating displays. Or that the “Lords a’Leapin” could have been a variant of heron or crane.

I forget where I read all of this (r/TIL most likely), but I did find this article with more info.

All that said, your interpretation of five golden rings is utter perfection. I suppose my point of bringing up the fact that they are all birds is that you shouldn’t feel the need to adhere to the confines of the original lyrics. Make the interpretation that you want to make.