I just moved my domain mail to Fastmail, and everything arrives perfectly. I'm annoyed that I was bullied into this by the fact that 'unknown' mail servers are third-class citizens, but at least the problem is solved.

Some paranoid thread in me fears that Google will find a problem with Fastmail's IP range and credentials this spring (among others), in order to consolidate the Gmail upgrade cash avalanche, but I'm hoping that's just me with my tinfoil hat on too tight.