"Snake pit" Modifier principles?

I have made a tangle of 15 hair strands, converted them to curves, and wish to use one object to be duplicated to follow each of these curves as paths.

If the main object was a snake this would result in a snake pit thing. By moving the snake (on the timeline), all the modified snakes would also move along their respective path, looking not realistic, but very organic and cool.

Is this even possible without treating each snake and curve as their own little “project” `?