Keith,
Very interesting. The 350 EW Sports did have a "special steering head damper", which I did not realize until just now when I read the fine print on the catalog specification. It cannot be seen in the catalog illustration; not even the tail strap that ought to anchor it to the top frame tube. That must have had some sort of universal clamp that went around the frame tube as there is no factory provision for anchoring it.
I suspect the damper was bought in. On the bottom I can see stamped "Patent Pending" which Douglas did not bother to do on their own items. In any event they never had a patent issued for a steering damper like this. They did patent the multi-plate type used on the 600EW and OC, as well as a contracting band and drum type. It does seem to have been made for the EW, as the cap that draws the collet closed is a parody of the standard steering head cap, including the slots to pass the control cables down through the center of the steering stem. The difference is the cap is in steel rather than aluminum and the height of the hex is much reduced, probably to save weight. The threads in the standard aluminum cap would certainly have stripped on the meager purchase of the little bit of thread that is protruding.
-Doug