That didn't work due to what I think is exim's weirdness about STARTTLS and TLS but https://github.com/peterverraedt/tinylist/ (which is a fork) did eventually work after much faff and experimentation.

One day short of 13 years sterling service and Ecartis has been retired.

Now that one is (assuming it works) perfect! Thank you! I have no idea why Google couldn't be bothered showing me that one in the many searches I did but I suppose I should have searched Github too.