Here's the solution - i'm a little unsure about it. It seems a bit too simple, almost goofy. It's just a belaying pin. Tie the string to a pin, and stick it in a little hole. To pull the string more, take it out and stick it in the next hole. It seems crude, but it has its advantages - it's easy to tie the string at the appropriate tension, and the holes can be exactly located after tieing the string to the pin. No accidental looseness or leeway with the line.

The disadvantages - i'm a little worried that reaching in and relocating the pin will be hard to do without moving the puppet's head unintentionally. Secondly, even with carefully located tiny holes, i'm only going to have about 7 frames maximum to execute a facial movement.

But who gives a shit - it works and it's easy. I'd like to be more robotic and less nautical, but hey. What can you do.