I figured out the issue.
All of us already HAVE the project on our systems, and there's this unexplained part of the process where you have to somehow convert your current project into the cloud repository . . . but then that local project is the one that won't connect. It seems you require us to ignore that perfectly functioning project, open up a brand new, blank project, and then pull down ANOTHER copy of the project. If I do it that way it works, but the "Master" version of the project that I used to upload to the repository in the first place . . . THAT one will not connect to the plugin.
EDIT: Although . . . someone else on our team had the same issue and the only way he was able to solve it was a reboot. I too rebooted before it ended up working for me. I just didn't think that was the issue, but maybe it was. Because they weren't trying to create the initial repository at all. They were working in a completely blank project, etc. So it's possible the real solution is just a reboot.