Rollo,
Yes the brake shaft does also take the reaction from the brake torque.
The brake arm shaft passes through the bushed lug in the front or rear fork, and the splined shaft engages the spline in the brake band bobbin. Working the brake arm rotates the bobbin and so expands the band and applies the brake, but further prevents the bobbin and so the whole band from being dragged around by the brake drum. Here the brake arm an bolt are new.
The backing plate is really no more than a dust cover and convenient place to anchor the brake return springs. It does not transmit any of the braking loads. It is a good thing too, as they are not very strong!
Here you see the opposite side with the brake arm 'plugged in'. This is an original brake arm; you can tell an original as they are usually bent!
As they used basically the same lever on nearly all models from 1925-1938 (they did get a little more robust as time passed, and some rear arms had a slight joggle to clear the frame), you should stand a good chance finding some to suit. Try posting in the parts wanted section. The new one shown above in the first image was made using a manual lathe and mill, plus and a file, so you do not really need anything special beyond having metal working machinery or a local shop or friend with same, and a sketch/drawing of an original brake arms to copy. I do not know if your particular model was one that used an identical arm front and rear. The shafts I think will all be the same.
-Doug
[update image links to https. 22Aug19 -Doug]
