I'm back, a month later, with an update.
We did all meet together in person. I was able to get clear communication from Cindy that whatever Betty and I do is fine with her, she's not placing any limitations. So that was a big relief because I needed to be sure there was no deception. There's not. ("Whatever" is okay as long as it's safe, and if other people are brought into the mix by any of us, we all inform each other, so we can each make our own decisions about health safety.)
Betty and I have had some rough times communicating, but finally figured out our style together. So we're moving along with our relationship, as it suits us. Cindy and I are totally different people, and it appears we don't have much common ground except for both being Betty's partners. And that's fine with both of us. The whole "triad" discussion is off the table. I have the kind of relationship I want with Betty. Betty has 2 relationships that make her happy. And by all accounts, Cindy is also happy.
Thank you again for everyone who helped talk me off a ledge a month ago!