The fire-engine had had brake linings retrofitted to the shoes, and that meant that the working diameter was wrong.
I changed the radius of the metal shoes to partially correct this (using my dad's horizontal boring machine), then bored out the relined linings to the correct radius to complete the job.
In principle you could remove the drum from the gearbox, set the gearbox up on a boring machine, clock true to the output shaft then bore the shoes to the exact diameter in-situ.
An alternative, though not so accurate, would be to wrap a spiral of emery tape round the drum and apply the brake. The problem is the lack of ideal inelastic zero-thickness emery tape.