I’m an avid user of Working Copy, the brilliant iOS Git client from Anders Borum. Apparently I still have a few things to learn about it though, as I discovered while listening to Episode 71 of the excellent iPad Pros podcast.
It turns out that in order to solve the problem of being able to browse and work with Working Copy repos from directly within Panic Code Editor (another iOS app that I use every day), Anders bestowed upon Working Copy a built-in WebDAV server. Fire it up, create a server entry in Code Editor pointing to the WebDAV server IP, and get to work.
The best case scenario is that when Panic updates the app, they allow direct access through Files app integration, since Working Copy can act as a Files location provider, but in the meantime, this solution works pretty well.