Aye, I've got a transitional mongrel too -I have a a Mk II (according to serial, and as per general appointments) with the old Meteor 'flying chevron' logo stamped to the fore of the cylinder.
But it has the standard scope grooves of the Mk III, rather than the 'crimped' examples of typical Mk I & Mk II. (no ''Meteor' lettering between the scope grooves).

It's also popping out just over 9ftlbs with standard BSA Meteor spring and shot to shot consistency is remarkable
Dreadfully heavy trigger though! (and its a Mk1 type trigger!) Despite much effort on my part, cannot get it to be entirely usable..
I need to find a way to sort that, and enjoy it more ...