The DT models originally they would only have a provision for mounting the footrest on the left-hand side. As these were converted for road use, owners would add a foot rest to the right-hand side, usually by gas welding a short length of pipe to the lower frame member. I have heard tell that only one genuine SW model can be documented as actually having left the Works, if so, then I suspect that at some point the factory started adding the footrest lugs to both sides on all frames, rather than build two different types. My 1930 DT/SW has brazed lugs on both sides, the right-hand side incorporates the rear brake pivot, a typical Douglas feature. This type of lug would need to be added prior to the frame being assembled.
Larger view
Larger viewIt sounds like on your frame, someone has gone to the trouble to wipe the lug off entirely. They must have had alternate plans for footrests that did not include the original lug(s) and wanted to save a few ounces of weight! You could simply weld a tube to the frame, fabricate some sort of clamp-on bracket, or replicate the original lug but split into two halves so that it could encompass the tube and then be sweated on with silver braze.
The large nut on the trans input sleeve gear is right-hand thread, as is the nut for the output sprocket taper. You do not need to remove the input sprocket to split the case to see what is the matter. But you will of course, to drop the sleeve gear out of the bearing. On the other hand, with the trans locked up solid, it will hold the shaft securely while you loosen the nut, every cloud has a silver lining!
-Doug
[Update https image links. 30Jan20 -Doug]