classic motorcycle forum

Can't shed any light on your particular bike but it doesn't at all surprise me. At the time Francis Barnett and James were being amalgamated at a great rate and the parent group, AMC, were going out backwards even faster.
AMC were always good at the parts bin shuffle producing 'new' or 'improved' models made up from the same old bits hoping to attract a paying customer. Your bike is a classic example. It's nothing new, just the same old stuff wrapped up with a different ribbon. In the same period as your bike they were selling in the USA another James/Fanny Bee lashup as the Matchless Pinto but it was still just the same old stuff but with a Matchless badge.
It didn't make any difference, the Japanese had arrived and this type of British lightweight just couldn't compete. This was the time when I bought my first Suzuki. It didn't just run rings around its equivalent British lightweight, it tap danced, sung the Hallelujah Chorus and played the ukelele while it did it. Riders took one look at what the Japanese offered back then and British lightweights were dead and buried.
I don't mean to sound negative. We love the old dears and they have their place in British motorcycle history and they are certainly loved in their old age but "rare" implies something exotic and mysterious and exciting. What you have is a curiousity, definitely not rare and exotic.
Cheers,

I told you Frank, once you get a lightweight another whole new world opens up!
Cheers,

Creaking bones and body parts not working how they should push many of us on to lightweights Frank, and like you we discover a new world. You've just joined the clan.
If you have a quick look in the VMCC Library you will see they have a reasonable amount of material on Montgomery including a 1939 catalogue which is about as good as you'll get. 1940 catalogues tend to be very sparse in content. My 1940 Matchless & AJS catalogues are each merely a folded sheet with one solitary bike illustration. I think they had other matters on their mind.
Further to the 1939 catalogue if you very nicely ask Annice, the VMCC Librarian, I'm sure she could find you find you the various announcements in the weekly magazines 'The Blue'un' and 'The Green'un' where they give details of upcoming ranges for the next year plus of course lots of stuff on Villiers, Webbs, British Hub Co etc.
The VMCC Library is a hidden gem for the sort of info you want.
As far as the paint finish is concerned I wouldn't be surprised if you have the remains of the original finish even if it does look awful.  We don't appreciate just how much finishes have improved since the 1930's. Our expectations today are much higher. Also of course a cheap bike had a cheap finish. You didn't get Brough Superior paint work on a utility lightweight like the Montgomery. 
Personally I'd think very seriously about mechanical restoration only and not worry to much about making it pretty. Lighweights seem to suit an oily rag restoration rather than a full concours finish. They were working bikes, not toys for weekend warriors.
Cheers,

Full strength Eucalyptus oil is good for removing burnt on oil. I used to get mine direct from an old boy distilling it but I don't know how you go in countries without eucalypts.
Cheers,

Hi again Ric,
Either Adam Higgins down in Gippsland or Keith Love of TinWest in Werribee will make you a set of guards. Even if you buy expensive ratty guards they will cost you more to get them fixed. The simplest & quickest solution is to just get a new set of guards made without all the mucking about.
As for wheels start off by having a chat with David in at Modaks.
You live in Melbourne, one of the most restoration friendly cities in the world. You can get anything done there.
Cheers,

German manufactured bikes are required to have an identifying plate fitted giving details of model, year, capacity etc. This is usually found on the headstock. It is more trustworthy than your papers and should help you identify what you have.
Cheers,

An engine number would be very helpful.
Cheers,