Saruman's Treachery

[Gorthaur the Cruel]

Another thought: if Gandalf had used Narya, surely Frodo would have felt it?

What an astute observation. But Gandalf as a maia may have added some extra mojo on that secrecy. My hypothesis is that Gandalf did not use the Red Ring until after he was resurrected as Gandalf the White. Why? Because simply as you have said, Frodo did not feel it nor recognized as he did with the Lady Galadriel. But did not Galadriel chose freely to confirm it herself?