I've no doubt that Enfield made some sort of Mk2 trial body or mockup just to see if it would be suitable, it would be a giant leap of faith to put the monotype group straight into mass production. I'm also sure they never even produced a complete gun, a toolroom mock up would be enough under the circumstances, after all, the mechanics remained the same.
As for the Enfield Mk2 production myth, its easy to see how the ED Enfield logo has been confused with the D daimler logo found on approx 25 to 30,000 early Daimler marked monotype guns.