I like the Noah Greenberg recording, but I would suspect the Decca Serenata recording from 1978, with Mark Brown, Pro Cantione Antiqua and the Landini Consort, may be closer to Munrow's intention... and may share quite a few of his musicians!
http://avaxhome.ws/music/classical/medieval/OxenfordDanielWhite.html (and scroll down a little!)
I often wonder how a piece of (relatively) obscure music such as this would be commissioned in the first place. Would Decca have detected a potential interest in releasing a recording of the play and then look to their roster of available artistes, do you think? In fact, do you think Mark Brown may have stepped in to provide Decca with a recording after their first choice of artist had sadly made himself unavailable?