Hey Oldmankit,
You have two problem here:
1 - Bluehost is probably blocking the SMTP ports on your shared hosted server. Which stop you from sending from the server of your choice (fastmail in your case).
2 - You're using a shared hosting to send emails which means that you'll always be on blacklists, no matter how much your readers will want to receive your email, there are hundreds of people sharing the same IP as you to send emails. The probability of one or many of them sending SPAM through their site is high unfortunately.
If you have a score of 7.5, that's not bad, so you could probably send your emails, but I'd definitely recommend you to signup for a 3rd party SMTP service in order to stay on the safe side. We have special integration with SendGrid and ElasticEmail allowing you to avoid your host SMTP blocked ports.
Hope this helps!