Hi Ben,
Thanks for getting back to me on this. In the end, I've ditched Bluehost. (I asked support and they said they can't unblock the port.) I've switched to Siteground, and am in the migration process right now. When the process is complete I'll enter fastmail as the 3rd party SMTP service. I've already got an account with ElasticEmail (through your promotion) so will check that too.
Thanks again!