Other comments are are good starts.

Another method would be to add a headers to the response:

    Server-Push: /relative/url

Then have an output filter pull them out and push them -- but AFAIK the APIs to do that don't yet exist in mod_h2 to push like that. Adding headers in the response is nice because it works with any 'backend', and the web server doesn't have to parse the HTML/css/etc going the through it.