Add a check that the Website is online to the WebTestSetupFixtureHelper after hosting the Website. It should use a configurable Timeout during which it tries to access the WebApplicationRoot Url until it returns 200.
This has several benefits:
We guarantee that the WebApplication is up in the SetUp and can fail early if it isnt up
The first IntegrationTest can work with an already started up WebApplication (as the first Web request on the WebApplication can possibly take a longer time than successive requests)