Is their a tool that can automate this enumeration process?
Not that I know of, but if you found yourself doing this a lot it might be worth creating one.
You can possibly script it with some bash.
I have tried to zip the interesting directory and copied it to my machine and I’ve been using grep with a certain ‘rocking’ wordlist hinted in this thread but so far the only thing I’ve managed to achieve is freezing my vm due to the grep errors because of unescaped characters in the wordlist. Am I on the right path or am I digging in the completely wrong direction?
You might have pulled down too much data but you are definitely in the right area. I don’t think running grep with a wordlist will get you what you need.