Mark,
From the looks of you generator drive arrangement, it would seem you have the 1937-38 type engine. This had the timing side main shaft extend right out to a plain bronze bush in the timing chest. The 1936 models had the main shaft stop short; the oil pump worm idled on its own stud in the timing chest, driven by a face dog (which was also the crank shaft nut). I have a 1936, and it can be seen here:


Forum member Eric S is working on a 1937-38 type; lots of pictures:
https://www.douglasmotorcycles.net/index.php?topic=6434.msg23959#msg23959I have not seen a handbook for the 1936-38 Aero models, but I do have a 1938 (non-illustrated) spares list. It lists the following:
18307 Timing pinion
18931 Coned hub for generator pinion
18929 Sleeve between coned hub and generator pinion
18944 Spring for generator pinion18930 Washer for spring
18213 Oil pump work
18309 Key for generator pinion and worm (presumably they mean the cone)
18310 Key for timing pinion
18099 Lock nut
18211 Locking washer.
Presumably the spring is a wave washer, given the restricted space available. Douglas had been using such on the 250/350cc engines to keep the engine rotary breather valve disk against its face, as can be seen here:


I suppose the change from the 1936 to the 1937-38 engine was to reintroduce some sort of slip clutch between the dyno and its drive, as they use to have on earlier models that were driven off the magneto gear. Using a bronze cone to drive is very similar to the friction tapping heads used by machinist in things like radial arm drill presses. Though the proportions do not look very generous.
As for the timing problem, the tappets are installed the wrong way, as you may have already noticed from the image earlier in this post. The faces of the tappet should be vertical. This kept the timing events truly at 180 degrees, even though the tappets are at an angle. Lacking a handbook, I don't have the timing figures for the Aero, but I would be very surprised if they differed much from the 600 EW, which shared the same layout. Figures seen here:

-Doug