A quick summary of our discussions over the last few weeks:

As discussed on HipChat, using Arquillian as in the Bean Validation TCK for instance would be a good fit, as we could configure the Hibernate Search container (Wildfly, none, maybe even OSGi?...) independently from the actual requirements of the test.
I know Hibernate Validator executes the TCK both in a Java SE environment and in Wildfly (Java EE). I didn't check how it's done, though; we'll have to investigate: https://github.com/beanvalidation/beanvalidation-tck + see how those tests are executed in Hibernate Validator.

The other question is whether this would allow to start external services dynamically (such as an Elasticsearch instance). This hasn't been determined yet, but the Debezium team is currently investigating on starting docker containers on-demand in their test suite; might be worth a look.
If we do that, one interesting option would be to run the custom, super-fast docker image Sanne built: https://github.com/Sanne/elasticsearch-light-testing

However, note that right now "Integration tests" means "almost every test", so switching to Arquillian would be quite a lot of work (since each test needs to explicitly declare each and every class required at runtime).