Consider removing / refactoring large integration tests

[rkm]

We have several large integration tests which:

• Take up the majority of the test suite runtime
• Are hard to maintain and very difficult to debug
• Re-tests a lot of code and behaviour already covered by the unit test suite
• Involve a lot of hacky bits for checking timeouts on message processing

We should consider whether these are still valuable and if we should keep them in their current form.