Is it possible to get a reference to a Playable Director from the Signal it emits?

Do you need the signal to be on a specific track?
If the signal is on the marker track, then it gets executed in the context of the Playable Director object, so you can always query the Playable Director component.

But otherwise no, signals don't provide backtracing to the Playable Director.

If you want to pass along the Director, or the length of the Timeline, you'll need to create a custom marker.

This tutorial I found gives a very simple explanation of how to do that in ~10 minutes