coaster wrote:You could try taking the trailing edges of the brake shoes with a file/sand paper, might help. Take care in case they contain asbestos

I believe that is the solution, as in normal running, there is one (bottom) shoe 'leading' & the other (top) trailing. When the scooter is pushed backwards, the roles are reversed & I think that the top shoe starts to act almost like a sprag & catch the drum surface causing a judder.
A stronger spring would help & I have resorted to making additional holes in the shoes to pre-load the normal spring so that 'off' is more positive on occasion.