I tend to run the tests individually and directly from my IDE (run->test in intellij).
I usually start with H2DatabaseIntegrationTest because that does not require any external database configuration or setup, and is significantly faster than other in memory databases even. When I want to run all tests, I will run all tests in the integration test package.
Having integration tests executable with little setup has proven to be difficult because of the reliance on testing all the way through the database. Having others get them working on their systems, however, will be very helpful since it will streamline the process.
Does it work for you to run the integration tests manually from your IDE?