Ok, I figured out at least part of the problem.
I don't know why it failed the first time, but it looks like failures
just cascaded after that, partly due to my mistakes. Even though I
deleted and recreated the domain, the cluster instances were still
running, which caused the new cluster instances to use different port
numbers, and the test was still talking to the old cluster instances,
on which the app wasn't correctly deployed for some unknown reason.
Once I cleaned it all up, the individual test runs successfully.
Now to try running the entire test suite...
Yup, that works. Just another transient quicklook failure...