Green men, Jack-in-the-Green, Wildmen have a history which is summed up by Sir Gawain's adversary: a magical figure, cosmic joker, riddler. He has something in common with Mediterranean quizzical myths and, purely imho, representations of Jesus from the gospels.

I think foliate heads are a more immediate figure, possibly Liz's Seth and the Beans that have fallen from common knowledge, on the basis that diverse church builders are unlikely to popularise paganism (or whatever the contemporary equivalent was) and Devils are shown differently.
There is a tradition of metaphorical heads in the medieval period showing toothache, migraine, lust, plenty, etc., which have no bearing on Rome's teaching and may be have local significance but no dominant transferable motif other than the foliate heads.