Yep, I just finished to setup a build and deploy system for Phoenix using edeliver and it's definitely not nice. A bunch of files in different languages, it feels unnecessarily hard. I hope that'll put some effort in that.
I host the production site I'm working on at Gigalixir[1] (with the postgres DB in Google Cloud) and it's been pretty sweet. Deploys have been trivial (the way they should be, if you aren't interested in also becoming a devops expert). Jesse Shieh is extremely responsive and a committed founder. Unlike Heroku, Gigalixir does not restart its servers nightly, which is very relevant if you store any state app-side (such as a cache).
I wasn't aware of Gigalixir, thanks for mentioning that. Looks very promising.
I've been hosting my site at https://clever-cloud.com with good results. I've been using Docker there but they just added beta Phoenix support which makes it really easy. They're French, and I'm in the US. So there have been time zone issues and support has been a bit lackluster at times, but generally they've fixed all the issues I've brought up and have been responsive. Price is right.
Elixir and Erlang deployments were tricky a few years ago, but I feel like now with distillery [0] it a lot better.
I use it in docker multistage builds [1] and have been really happy with that.
[1] https://gigalixir.com/