I hear you mate ... however British rifles can be found with the MKII's and they can end up with anything depending on where they've been and what kind of civvy life they had. Some people keep the better Mk1 Singer when they sell a rifle and replace it with a MKII just for sale.
I see probably more Enfield rifles than most over at Surplus rifle and with people constantly wanting rifle Id's I have learned one thing. With Enfield rifles there's always exceptions to the rule - I try to keep an open mind until the evidence is in.
I'd say if it's going to be North American manufacture at all, it will be Longbranch. But as yet can't say 100% for sure ...