So I opted to just go with a hand towel ring since this is just a half bath, and a small one at that. There just wasn't a need for a big ole' towel taking up all of that room.
Yay! We have a working toilet paper ring (aka Silas' new favorite toy, he loves seeing how much toilet paper he can unravel in 20 seconds. Let me assure you it's quite a lot) - no more toilet paper on the floor (unless Silas has just been in the room).
Things are looking nice and bright in there these days. More things to come.