Quote - There is one solution: making the rings a conforming figure with the relevant JCM's and the classic breast morphs included.

Yes, and I did consider doing that. Fortunately jancory's solution of parenting the rings to the chest seems to have fixed the problem. Where I made my big mistake was in not testing thoroughly enough before posting. I tried a few stock posed on the figure, and when all seemed to work OK, I uploaded the file. With hind sight, it is obvious that none of the poses I applied moved the collars, and I should really have tried applying manual rotations to them.

As to the Breasts-classic and Nipples-classic morphs, they are catered for, and when those morphs are are expressed in Antonia the rings should adjust automatically. This works for me in P6, I'm hoping it is working in other Poser versions. Even though the rings are props, they use the same "super-conforming" method as conforming figures do. There are 10 PBMCC channels in each ring and the control prop, so it should be possible to cater for other breast morphs via injections.

Quote - for a more pemanent solution use a Python script that takes the co-ordinates of the nipple vertices...

That sounds very interesting, and I would love to know how to do that, but my knowledge of Python script is virtually none existent.