Oh, how could I forget!
Of course I can't set up testing from the TestFlight web portal, because that would just be too easy, right? When I try to make a new test, on the screen where I can type some notes to the testers, when I click "Submit for Review" I get the error message, "There was an error processing your request. Please try again later."
So helpful!
The only way I can't set up tests, internal or external, is with the TestFlight on an iPhone, but nobody can install the app!