Have you reached out to FM support? I have one $50 account at my custom domain and neither of those problems are issues for me at all. It always defaults to my custom domain, and I log in with my custom domain as well. I have several other aliases and domains that I can use as well, but those are not the default (and I've never used the @fastmail domain).

Support has always been very responsive in my experience. I'd try them first.