Hi,
As I said previously, the crack looks to be at the joint of the top tube and headlug. From some of the photos taken in the Douglas factory, it looks as if Douglas used an early form of gas welding on this joint. With this in mind, I would suggest that it would be a good idea to 'V' out the crack - firstly to remove any of the old 'braze' - as you don't know what grade of rod was used, and secondly, to get full penetration with the new weld/braze. If this process leaves you with clean steel right to the root of the 'V', you may be able to get it TIG welded but it is likely that the weld may end up porous due to impurities in the parent metal caused by the original gas welding operation. I still prefer the idea of a brazed repair - if you are worried about the strength, you could use a Nickel bronze rod instead of silicon bronze - these rods are about twice the price and not often available in small quantities.
Whilst you have the bike dismantled, it would pay to check out the lower top tube for any similar defects. Should another crack be found, it might pay to saw on round from the cracks so that the frame can be sprung open to insert sleeves into the tubes to reinforce the repairs.
As always, repairs on 100 year old motorcycle frames can throw up unexpected surprises, but good luck anyway.
Regards,
Eddie.