YB,
Your ideas re Lord Bateman. Already tried. As an ardent young folk song field collector in the 60s I went to record an elderly lady in a remote coastal village with a large repertoire. Having just recorded a version of Lord Bateman from another elderly lady I asked Ethel if she knew the ballad. Not to be outdone she came up with the following to her own tune on the spot.

'Lord Bateman was, he was, he was,
He was, he was, a bloody fool!'

She had a wonderful sense of humour.
BTW her close neighbour sang a great version of 'Mutton Pie'!
There is a recording of a version of Mutton Pie titled 'The Yorkshire Farmer' on the Yorkshire Garland website. This version hasn't a chorus though.