To quote our Doug "Well it may be more complicated....."
Thats very true, The frame number XF668 fits exactly into the E29/F29 series, there are 22 of these on record and 668 sits more or less in the middle, the engine number EQ863 is definitely from the S6 models, whereas, the gearbox number WG2546 fits comfortably within the E29 range. The S6 series although similar, almost all those on record have the prefix WG/T****.
The fact that the engine fitted has the number EQ2546 which matches the gearbox is an amazing coincidence!! the EQ designation is S6 whereas the gearbox is E29, making the match very unlikely particularly as Douglas did not normaly match them (until the post war Dragonflies). My knowledge is insufficient to advise accurately but it may be worth comparing the detail of the two engines, I am sure someone with more detailed information will tell you the differences between an E29/L29 (500 & 600) engine and the S6 EQ series engines. You would then be certain which engine is actually fitted irrespective of the number stamped on it! Sadly our records do not list the gearbox number of the machine with the frame number XF668.
One tip for clarifying unclear numbers that can avoid scraping off the paint is to take a "brass rubbing" this is done by holding firmly a thin piece of paper over the frame lug or crankcase and rubbing a soft pencil across the number. The result can produce a surprisingly clear white image on the black background.
Good luck with your search for the history of the bike, but take my advise, don't worry too much, the bike looks good and is there to be ENJOYED!