Hello Again,
Thanks to all on the suggestions on how to deal with automatic inlet valves and the lack of original specifications for the Douglas. It looks like trial and evaluation is going to be my lot during the first season of riding this bike.
As Doug wrote "So 2 degrees before TDC sounds to be right in the ballpark",
or as Leon wrote "in which case the 20 degree after TDC may be a better option",
indicating that a definitive answer is not forthcoming so a bit more research is needed.
I measured the dwell of the cam with 0.006" clearance to be between 235 and 240 degrees, then found the specifications for two other Air-Cooled engines with automatic inlet valves.
Gnome 90 HP Rotary: Dwell 258 deg, Open 65 deg. Before BDC, Close 13 deg. After TDC
Franklin 12 HP 4 cyl.: Dwell 237 deg, Open 38 deg. Before BDC, Close 19 deg. After TDC
The Gnome is a strange engine by anyone's standard and the designers were mainly concerned with the maximum full-throttle power with the lowest possible weight so its very early Exhaust opening is probably not the best analog for the Douglas. The Franklin, on the other hand, is very similar in dwell, purpose, and general layout to the Douglas. Plus both Franklin and Gnome call for a fairly late Exhaust Valve Closing. The piston has not really moved down much even at 20 degrees so the thought might have been that you want to make Sure that there is NO residual exhaust pressure when the piston starts moving seriously so that the inlet valve opens promptly.
So I have set the exhaust to close at 20 degrees after TDC and will give that a try. If the performance is lacking (and after trying other aspects of the engine), I will move it one tooth earlier and try that. After all, working on an old bike is almost as enjoyable as riding one.