Post making contest 6.0

There might well exist a set of three heads that's sufficient, but it's not ours.

Mostly this is because in general I'm not fond of big and vague puzzles and that's two out of the initial set. At least I was able to cut to the end of one of them once we had a few key parts of the clue figured out.

We just aren't getting anywhere with 4, though.

Passes none of the rules