I thought of another "solution" but it's not actually working in its simplest form.
Given your theme is plain CSS and doesn't require LESS compilation or access to Flarum variables, you could just include it directly as a separate stylesheet by using @import ""; in the custom LESS or adding a <link rel="stylesheet" href=""> in the custom header.
The problem is that raw file from GitHub are served with text/plain MIME type and Firefox and Chrome (at least) refuse to apply a stylesheet that doesn't have the proper MIME.
One workaround would be to publish the repo as a GitHub Pages site, then access the stylesheet as https://yourusername.github.io/reponame/flarum.css. This should have the proper MIME.
Caching issues might give you hell with that solution though ? not sure if/how GitHub Pages caches static assets like CSS.