For the remaining clue:
We know it also goes by another name, that is perhaps more popular, but not used more often by JRRT.
The answer could have been "beryl" (is it because it could fill the R in the password, or because it actually answers the clue?).
It's in a song.
Yes, I am working with JRR BLING as the password because it makes more sense than anything you get with a vowel in that place.
I am finding myself quite short on ideas. Can it be another Ring of X? I cannot see how you can solve this clue cryptically. Literally, most Rings were desired by more than one person. RING OF BARAHIR, which was only really desired by Beren when he stole it back from the orcs? But what's the other common name for it? And what song is it in?
Or something like RUBY, to match the beryl and garnets.
I don't know.