I've probably missed something but is there a chance that someone has 'acquired' a later un-numbered Lithgowno-cut off body and made it up, say, after the war using an old worn out BSA as a donor for the parts.
I say this because the lower legs of the '939' in the 1939 date look like they are more modern 'unhooked' format and the lettering looks a bit uneven as opposed to a roll-stamp or made up impact-stamp although we can't see it very clearly.
I know this is hardly a forensic analysis but re-bodying is one thing for your damaged £15,000 VW Golf but re-bodying at a Field or Base workshops or even at a factory for a £13 rifle (the Ordnance VAOS list price of a part worn No1 Mk3 in 1965, when a brand new No4 was list priced at £22-10 shillings) isn't the kind of economics that would keep you in business for long. It's like putting new uppers on your old shoes
Or am I missing something