Well done finding a frame! Finding a gearbox, in comparison, ought to be a breeze.
But... The OB/OW gearbox shell is very short in height to fit in the limited space above the rear cylinder. 4-11/32” from the mounting surface under the seat to the bottom of the housing. I know of a hybrid OB which has the 1928-30 DT/SW gearbox fitted (TG, UG, and YG prefix ‘boxes.) This shell is a little taller, 4-31/32”. It is a tight squeeze between the bottom of the shell and the rear spark plug; indeed I believe plugs with short insulators are required. The DT/SW cases are a little easier to find; however finding one with decent internals is a different matter! The other difference between the two is the OB/OW ‘box has the lay shaft and shift fork to the front, and the DT/SW has the lay shaft and shift fork at the rear. But this just means making up a different shift rod and chain guards, no permanent alterations required. More serious is a slight difference in the primary chain line. But on the afore mentioned hybrid, this was solved by making a new hub for the gearbox input sprocket to step it out slightly. It was not very much.
Many of the vintage sprinters do use a Norton gearbox to get four speeds and quicker shifts. The box used is the upright Sturmy-Archer design, known as the ‘dolls-head’ gearbox. Not sure of the years of production, but be warned there are variations. I found this out when I purchased a box of bits. I got a plain bearing lay shaft but a case that used ball bearings. Obviously the ball bearing version is preferred, so you probably want to stay away from the earliest iterations. There was also a later variation with a sleeker upright end cover containing the positive stop mechanism, and I think much the same internals, before the AMC style gearbox came out.
To use in the Douglas this ‘dolls-head’ box is laid down and a mounting pad to suit the Douglas frame is welded to the formerly back face. A bit tricky to minimize distortion. It is also very important to provide steel keys (like Douglas did) to take the shear of the chain loads trying to twist the box in the frame. Otherwise it is reported the studs tend to work loose or put out of the gear case.
I think most then use the Norton clutch and abandon the Douglas flywheel clutch. This box is 4” to 4-1/2” in depth, depending on where you measure, with some bumps jutting out even more. So it may be a tight squeeze in the OB frame as well. The DT/SW frame has a bit more distance between the engine rails and the gearbox mounting platform, I believe.
-Doug
