The problem is package managers aren't consistent across distributions. If you want to provide a binary version of your app, you should be providing at least .deb, .rpm and tarball packages.
In practice, everyone's just targeting Ubuntu and publishing .debs.
Thanks for the encouragement! I might take another shot at it sometime. I had this server running for about 3 months with just my personal mail, sending probably 1 email per day on average. It's possible slightly higher volume would do a better job of "warming up" the IP.
I self-hosted from about 2007-2008 and 2011-2013, and had nowhere near as much trouble with deliverability. It came as a bit of a surprise how much more difficult it is these days.
I was actually hosting on Linode (UK). My hunch was that they would be one of the more reputable networks; I've run small mail servers on them before (2+ years ago) without any problems.
It's a pity there's no easy way (that I know of) to look up the reputation for an entire network block. I'm glad to hear your experience with Linode matches mine.
In practice, everyone's just targeting Ubuntu and publishing .debs.