In Norwich there's a Morris side called Kemp's Men, formed in honour of Will Kemp and his long dance from Norwich to London. I've followed them for years, so I've just send them an e mail asking if they have any knowledge of the origins of the jig.
Norris Winstone MBE was their extremely knowledgeable musician, and although he died a few years ago, he may have left some sort of information about the jig which some of the present side might remember.
I'll report back if/when they reply.

By the way, in May 2015, Rick Jones Morris danced the whole distance (he was 58) in imitation of Kemp's 'nine daies' wonder'. Police tried to arrest him at one stage. They thought he'd escaped from a mental hospital!