Hi Jason,
1. I think I will need a test suite with the test classes in
src/main/java (rather than src/test/java) so that the provider can get
those classes onto its own classpath during testing. Will Arquillian
work OK like that (ie: does it have maven integration which specifically
looks under src/test/java only)?

No, there's nothing in there that I'm aware of that would prohibit this approach.
You're right of course. The thing that seems to be getting in my way is actually the Surefire Maven plugin. I've created the TCK project separately and configured the Compile plugin to generate a seam-cron-asynchronous-tck-tests.jar which I'm then including in the asynchronous provider's project like so:

        <dependency>
            <groupId>${project.groupId}</groupId>
            <artifactId>seam-cron-asynchronous-tck</artifactId>
            <version>${project.version}</version>
            <type>test-jar</type>
            <scope>test</scope>
        </dependency>

However Maven still concludes that there aren't any test to run for that project. I suppose that's for good reason, but I'd like to work out how I can have these imported tests run by Surefire, rather than just the ones in src/test/java. I'll keep trying but please chime in if anyone has any ideas.
2. The classes in the test suite have a hard-coded @Deployment, and I'm
not sure how I'd go about customising that place a different provider
class on the classpath. I don't want to have to force my providers to
extend every test case just to customise the deployment.

You're @Deployment should be in the test class, but that doesn't stop you from having a base method that setup everything and just returns an archive you can add to, or even merge(...) in your @Deployement method.
Would this require me to extend each of the TCK test classes in the provider project, in order to be able to add to the archive returned by the base method? This is something I wanted to avoid (even though it would clearly solve problem 1).

Cheers,

Pete R