1. Configure the in-memory Hydra instance with a null path input cache
time to avoid caching slowing the test down.
2. Use the Catalyst::Test helpers so we talk to the application and skip
needing to actually run a webserver.
3. Change path references to use a tempdir, since this is running while
other tests are also running.
4. Change the login flow to save a cookie and pass it manually. A bit
weird, but it avoids a dependency on heavier browser-mimicking
libraries.