There is no "more" option after tapping "music" so I don't know how to access the home sharing library

I had this same issue as you and technically am still having it. Video's from home sharing show up almost immediately (prompt opens to select library immediately due to no videos on iPad) but with music there is no "more" button. To get around this i put ONE of my 2000+ songs on the iPad, then i had the option to click up top where it says "artists" (or songs, albums, genre, etc.) and go to home sharing, and select my shared library. I find it extremely annoying to have to have a song on the iPad for this option to show instead of just having it auto-prompt like the videos did. I hope this helps you find a way to make it work for you, and help Apple fix this annoying issue.

You sir are a genius. I have been trying for days to get this to bloody work. 😁