The Romans didn’t necessarily draw the distinction between serious and comic that you’re drawing - the possibly-related Fescennine Verses, for instance, were both ribald and profane and intended to ward off ill luck.
As for the mediaeval examples, one theory is they’re related to Carnival culture, and that others are mockeries of specific normal pilgrim badges (e.g. one depicting a ship of dicks being in imitation of the Thomas-Beckett-on-a-ship badge)
I was mightily confused for a couple words there whether “she” was your sister or your sister’s dog. Then it became obvious. Pronouns are dangerous shotguns.
It does, quite well. “Richard [the Third]” means shit in the specific sense of the countable noun “turd”. So it’s either a satchel of dicks or a satchel of turds.