Have you implemented DKIM/SPF/DMARC? If you have not, that is a first step.
Are you sending from a "consumer" network IP block (cable modem or DSL)? If so, that's going to be big points off (probably not since you are sending through fastmail).
In my limited and somewhat dated experience, some email service providers are very aggressive in blocking email senders. The better class of these had contact information and would respond to requests to be whitelisted. Some email providers blocked emails and had no contact information to request white-listing. For them, my only recourse was to send emails to them through an email forwarding service (I used Dyn at the time, Dyn apparently sold their email forwarding business to DuoCircle).
https://en.wikipedia.org/wiki/DMARC