Steve,
You are discussing items that can be added on to a road bike. While those components might be of racing origin, perhaps even Works, their presence does not make the remainder 'Works'. Initially you said it was definitely a racing model, perhaps a Works model. Now you mention the engine and frame codes prove it is a factory Works machine. Have you received new information that has solidified its provenience? As I mentioned, those codes are assigned to the F/G31 models. Physically the components match the appearance of F/G31 models, as does what can be seen of the gearbox (which you should find a prefix code of AAG/ wide-ratio, or AAB close-ratio.) So far as I know, the codes for the thirties Works racers did not survive, so if you have a source for that information, that would be fabulous addition to the Douglas history.
From what I have seen of photos of the Works racers, and the three or four Works survivors, the frame, engine, and transmission you have do not have the characteristics of a Works racer. By that point what the factory was racing and what they were selling the public was distinguishably different. Deep, finned sumps; reinforced DT/'26TT 3-speed gearboxes (cross-over) followed by a purpose made Sturmey-Archer 4-speed gearbox and external positive-stop foot change; larger heads with wider splayed valves; panier petrol tanks (on the Senior machines); taller headstock, cross-over brake shaft behind (not through) the down tubes (once they went to t 4-speed). Douglas did not go racing with the enclosed valve gear heads, as originally those were configured with a single carb. That would not stop a privateer from putting twin carbs on one and having a go. But back in the day there would have been plenty of ex-Dirt Track Dougies about that would have already been setup for twin carb and high compression, and so would have been less work to go racing with.
There are a lot of Douglas racing replicas about, including several replicas of Works models, so I certainly agree it is worth getting it right. Something about the Douglas make it a favorite to model into a racing machine, and to this day they are popular in a stripped down version with Norton gearbox among the vintage sprinter crowd. You cannot be too careful with your research, as the value between a replica and the real thing is about four to one.
-Doug