What you describe is exactly what I'm building - https://songsling.io

Didn't want to explicitly promote it here in the thread, but I'm building it to serve as a general music-content engine for artists (also for my own music, let's be honest) that will let you upload composition parts and the player will put them together on the fly. It already has interactivity built in where you can serve a different version of a track based on changing inputs you connect from your Internet presence etc. Plus, you can DJ with it, it supports smoothly changing playback speeds. It needs to happen.