Let us not also forget that because this printing is the one that survived doesn't mean that it was the first printing. It could even have come from an earlier manuscript.

Meanwhile a few more Edward ballads (Not to mention Percy's concoction of that name)
Roxburghe has 'A New Ballad of King Edward (IV) and Jane Shore' already alluded to.
Well-known is '(Dialogue between) King Edward the Fourth and the Tanner of Tamworth'
'King Edward's Ghost, or The King and the Cobler' See Bodleian, Harding B3(4)

I think this make's your Edward IV favourite.
During the height of 'historical' ballad making, i.e., 15th-16th centuries, many new ballads were based loosely on old legends, e.g., most of the Robin Hood ballads. Why should this be any different?