Jeff. Did you ever get hold of a rear brake plate? Don’t get excited, afraid I haven’t got one, but have you tried the Brough Superior owners club? Brough certainly used compatible brake shoes on the front ,as one of our members kindly told me, thus ending a two year search. It could be worth a long shot for something that just needs a bit of alteration. Their spares man is v. helpful.
Sorry I took so long, but the new site had my limited brain power foxed for a while.