What happened to the WW1 surplus 2 3/4hp machines?
I can add a couple of things to my reply above.
It's worth mentioning "The War Motor Association" which was set up around June 1919 "to enable ex-officers and men to purchase those not required by the Government at a reasonable figure". There are a couple of articles in The Motor Cycle about this organisation (e.g. the editorial 19 June 1919), and it is mentioned frequently in small articles about the disposal of motor cycles. That said, it's not clear that it was very successful because a common theme in letters to the editor is that machines being sold were beyond the means of many returned servicemen.
Also in the The Motor Cycle is quite a lot of discussion about the "new" Douglases sold in crates. It turns out that many/most of the crated bikes were NOT new, but were "unissued" - renovated at Government workshops but never put back into service. One writer (who signed himself "Retyred Hurt") bought a new/unissued Douglas at one of the 1919 sales and was disappointed to find that the front tube had no fewer than eleven patches! Not to worry: it was so badly perished that it needed replacing anyway. "Considering that the Government were supposed to be putting an end to profiteering, is it quite reasonable that they should be allowed to mislead the public, with the result that they are paying between sixty-three to seventy guineas for second-hand 1914, 1915, and 1916 Douglas machines?", he asked.
Finally I can shed some light on how Burlington's, who renovated and sold large numbers of WD machines in the early 1920, sourced their machines.
In the middle of 1920, the Slough Syndicate, headed by Sir Percival Perry, purchased 3,000 ex-WD motorcycles, and announced three "Sole Selling Agents", one of which was Burlington Motor Co., Ltd., Clapham. Interestingly the machines were said to include "Douglas 2 3/4 h.p., Douglas 4 h.p., P & M, Clyno, Enfields, Royal Rubies, etc. etc..." - no mention of Triumph (whose numbers should have been similar to Douglas). Perhaps the story that Triumph did their own renovations and resale might be true.
Still nothing found to suggest that Douglas was directly involved in renovation, but in September 1919 Douglas Motors Ltd reported that they had been "inundated" with orders for spare parts "as a result of the Government disposing of many thousands of incomplete machines..."
Leon