I self-host my Jekyll-based blog, by compiling each push on builds.sr.ht and rsync'ing it onto a static web server. Basically roll-your-own GitHub pages. I also wrote a tool which converts your Medium posts into a Jekyll blog.
Have you considered building https://cdn.sr.ht? I do a similar process for some sites and use AWS CloudFront to essentially get globally deployed static sites.
Since this is a workflow you've encountered might be something that people would pay for. I definitely like a CloudFront alternative that wasn't as overpriced.
https://git.sr.ht/~sircmpwn/unmediumify