Depending what you find acceptable there are things you can do. For example at work we proxy through a mailgun account to do simple smtp notifications from bash scripts and webapps.I would imagine you could also proxy from an email server.
And you can at least manage your own email domain accounts via various webhosts. This may not meet your criteria for self hosted but its more independent then using gmail.
I suffer the indignity of having to open the shower door and reach out to the counter for a sip. I suppose I could do that for a reuben too, but that seems like a bridge too far.