This is an extension I'd use once in 5 years. Boy am I glad this exists when that time comes.

What this does:
1) You must be logged-in to your youtube channel
2) This must be added on your browser bar
3) Click on it
4) Click on the button to take you to your watch later list
5) Click on the button to clearn

This will automate removing videos from top to bottom. Go away for a bit and run it again.