Greg, I think that it might also possibly originate from Cheshire, or was at least current in Cheshire, I remember a pamphlet of Cheshire folksongs in the 1970s - unfortunately mislaid with moving houses several times over the years. It was just called Cheshire May Day Carol I. It had an additional verse:

Come forth the maiden of this house all in your gown of silk
For the summer springs so fresh and green and gay
For you are worthy of a man with forty cows to milk
Drawing near unto the merry month of May

Perhaps someone else knows of the pamphlet? It also contained a second Cheshire May Day Carol II, Marco and Pedro ( I think this originally came from a broadsheet published in Manchester) the rest I can't remember at the moment.

Maybe it could fit in with the boat theory as Chester was a major port until the Dee silted up too much?

Ian Lever, Red Lion, Malpas