. . . there is one flaw in your argument about Snape telling Voldemort that his ring Horcrux has been destroyed. First, there isn't any place in the book that tells us that anyone but Dumbledore and Harry (and Slughorn) know anything about Voldemort creating Horcruxes. Voldemort, of course, hinted at it in GOF when he told his Death Eaters that he had taken more steps than anyone towards trying to achieve immortality, but it doesn't sound to me like he has actually told any of them what the steps were--otherwise, Lucius would not have given away the diary. (And thinking about Voldemort and Dumbledore's description of him being a loner and not truly attached to any other person seems to back that up.)
Now, in Spinner's End, Snape goes through all the reasons Voldemort trusts him, Dumbledore trusts him, and why Bella isn't so trusted anymore. Yes, I agree Severus thoroughly enjoys pointing out to her that her once lofty position is severely diminished. However, Snape never mentions that it was the ring or the destruction of a Horcrux that caused the damage to Dumbledore's hand:
Chapter 2, p. 31 (US):
[Snape says]--"I am pleased to say, however, that Dumbledore is growing old. The duel with the Dark Lord last month shook him. He has since sustained a serious injury because his reactions are slower than they once were. But through all these years, he has never stopped trusting Severus Snape, and therein lies my great value to the Dark Lord."
There are a couple of interesting things in that passage. The first is that he is telling her that Dumbledore is growing weaker and that is what he has told Voldemort as well. Snape also acknowledges an additional injury to Dumbledore but misleads her into thinking it is just because he was shaken by the confrontation with Voldemort--there is no mention that it was due to a powerful curse placed on a ring that was a Horcrux. There is nothing in that bit of information that tells her anything about the real truth of Dumbledore's injury.
We don't even know if Severus actually knows what caused the injury to Dumbledore's hand. For that we need to look at the chapter where Dumbledore explains the concept of Horcruxes to Harry. In Chapter23, p. 503, Dumbledore is telling Harry that he destroyed the diary Horcrux and that he (Dumbledore) has destroyed another one.
"Yes, indeed," said Dumbledore, and he raised his blackened, burned-looking hand. "The ring, Harry. Marvolo's ring. And a terrible curse there was upon it too. Had it not been--forgive me the lack of seemly modesty--for my own prodigious skill, and for Professor Snape's timely action when I returned to Hogwarts, desperately injured, I might not have lived to tell the tale. However, a withered hand does not seem an unreasonable exchange for a seventh of Voldemort's soul. The ring is no longer a Horcrux."
The only thing that tells us is that Snape knows that some powerful curse caused Dumbledore's injury--it was the curse that caused it, not that the ring itself was a Horcrux. Dumbledore doesn't say that he told Severus anything at all about the Horcruxes. Until Harry got the memory from Slughorn, Dumbledore didn't mention them at all--so why would he tell Snape about them if he wasn't really sure what they were dealing with? I don't think he did. We know from past visits of students to Madame Pomfrey that she doesn't have to have all the details of an injury to heal it--(when Ron went to her with his injured hand when Norbert bit it and it was a nasty wound). All we learn is that Snape was responsible for saving Dumbledore's life--which isn't what he tells Bella either.
Now the other thing is--would he tell Bella something that is different than he had told Voldemort? Not likely. She'll run right to him to confirm Snape's story; he'd better be saying the same thing to both of them. So if he told Voldemort the same thing about Dumbledore that he told Bella, then Voldemort doesn't realize that it was a Horcrux destruction that injured (and nearly killed) Dumbledore either.