I think Rings had little to do with Saruman's breeding programme; he would have done this anyway. I do agree he probably took human women and male Orcs and had them breed; possibly women of the Dunlendings or Rohirrim women captured in the Westfold? I am also sure that Orcs and Men could breed; taking the possibility that Orcs are corrupted Elves, we know Men and Elves could breed, so why not Orcs, if they are/have been Elves?
I also think that Orcs would relish the possibility of breeding with women, distasteful as it sounds. Tolkien took great care not to mention what happened to Celebrian when she was waylaid, but the possibility of something incredibly horrible happening does exist. The absence of an explanation can often speak volumes.
Anyway, about that pesky Ring again. I have in my mind a picture of that ring. I think it may be constructed of crystal, may include some kind of Prism. This would make it a genuine
ring of many colours for a
wizard of many colours. It could have been an inspiration for, or perhaps inspired by, Saruman's Light Breaking. It may even have been a tool for what he was trying to attempt in breaking up that Light/Divinity to see what it was made of.
I also noted how Gandalf seems almost to dismiss this ring of Saruman's as a mere trinket. I wonder whether Gandalf really thinks that? Was he trying not to give Saruman and his craft any credence? One of the ways the true Rings of Power seem to work is by reputation; even just to hear of one evokes fear and passion. Maybe Gandalf feared the Ring of Saruman taking on this kind of life, the same type of reputation as the One Ring?