Hi Alistair, welcome to the forum!,
Until I read your post I had not realised the balls for the hubs on the 2 3/4 HP were listed as 1/4". All the hubs I have seen have eighteen 5/16" balls in them (9 each side). The Handbook of the Douglas Motorcycle 2 3/4 H.P. 1925 lists the ball size as 5/16".
The cups and inner screwed dust caps usually have "L.H." and "R.H." marked on them to indicated (obviously) left and right hand threads. You have assumed correctly that the R.H. cup screws all the way home in the hub and the R.H. inner dust cap is screwed onto the exposed thread. The L.H. cup is then screwed into the hub and adjusted correctly, then held in place by the lock ring. The L.H. inner dust cover is then screwed onto the end of the L.H. cup.
The inner dust covers have a "TO UNSCREW" direction arrow on them but it is quite often hard to see or has been worn off completely due to use.
The outer "tin" dust covers and the washer to lock the axle to the fork are quite often missing.
I have not seen 1/4" balls used in the 2 3/4 H.P. hubs. Also it does not appear that the balls are listed in the early parts lists (i.e. pre 1922). Maybe a forum member has experience with 1/4" balls in these hubs?
Cheers
Ian
Images converted to linked files - Dave, 13Jul2021