I was led to understand, regarding the 'Martin said' verse, that the Man in the Moon represents Henry 8th (from his round face, presumably) and his 'clouting (ie mending) of St Peter's shoon' refers to him patching up his differences with Rome, about as likely as the other things Martin sees when drunk.

The verse certainly goes back to Elizabethan times (it is in one of Ravenscroft's books of 'old songs' published before 1610) and any dig at King Henry would have to be obscure. At least the explanation makes sense.

Andrew