My Father-in-law has a bigger machine and a business meeting took me close to his workshop yesterday so I took the parts along.
The drum was attended to first with just a light cut to clean up rust and scoring.

Then I was able to put the back plate in complete with the shoes to skim them to a nice fit with the drum.

It didn't take much to get the parts to fit but the linings are now well matched to the diameter of the drum.
If I'd remembered that this was an almost irreplaceble early style drum and back-plate I might have been a little more nervous doing the job. Thankfully that didn't occur to me until afterwards..... :-)
With that job done I am free to get on a build up the wheels.
G