The brake should certainly be better than that! When you had the shoes out, did you check the diameter of the brake drum? It should be exactly 7" dia - if the drum has been skimmed, you will need to either file some off the centre of the linings to aid bedding in (but be careful not to inhale the dust), or unrivet the linings and insert a shim under them to bring them out to the diameter of the drum. As I said previously, centralising the brakeplate improves the braking - in some cases it is necessary to open out the hole in the centre of the brakeplate top hat bearing with a small grinding wheel to get a little more adjustment.
My Dragonfly is fitted with Douglas brakes the same as yours and will make the front tyre squeal if I take a good handful of the brake lever! Oh, and I'm using the non asbestos linings supplied by Friction Services of Bristol - from memory, I think the code number is 3806 for that material.
Regards,
Eddie.