Continuous- Compact Strips

Hello all. I am new to this site and decided to join due to my love of Music boxes and my recent desire to start creating them. Eventually Imma try and create cylinders due to their compactness however this is an obvious start point. I wanted to make a couple projects but both projects would close off the music box. Making it Impossible to Re-Feed the paper through when the song finishes. Im curious if anyone has found a way to circumvent having to re-feed. Or maybe theres a completely different way that I'm not thinking of? I'm sorry this post is slightly scattered but I appreciate any help you guys can give. Thank you.