If you're planning to offload to a third party anyway, why don't you instead first try routing mail though AWS SES? You'll definitely get better delivery and at least you'll be able to control the rest of the stack.
(I actually already have a Fastmail account, and I use it to deliver mail to domains where my server is blacklisted. But even that little concession feels like defeat.)
Not sure about better, just different since it's strictly an MTA. But perhaps you can also use Fastmail as an MTA only? Biggest benefit I can think of is with SES, Amazon would never see any of your incoming mail. Well, unless you replied to something. Then I suppose they would have access to it indirectly.
> perhaps you can also use Fastmail as an MTA only
Yes, and that's what I actually do to solve my current problem. But one of the reasons I run my own email server is to maintain my claim to fourth-amendment protections in light of Smith v. Maryland so I really don't want my mail being routed through a third party.
there are also small companies which deliver the same service, if that appeals. i've been using mailroute.net for delivery and spam prevention for a small business for years.