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.)
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.