(I’m thinking out loud - maybe answering my own question.) I guess the issue is more that ONLY REPUBLICANS should be able to VOTE in the Republican primaries, so getting the names on the ballot shouldn’t be as difficult as they seem to be making it.
Virginia does not have party registration. It used to be a Democrat one-party autocracy. They didn’t imagine it’d ever be necessary to register Republicans.
Virginia doesn’t maintain voter party affiliation. That’s why it’s an open primary.