Hi Kevin,
You don't appear to be having much luck with rear brake pedal, so just a thought. Ithink you'll have to stick with a cable operated brake, so here's a suggestion. Most BSA (some) models of 50's and early 60's had cable operated rear . brakes, plus they were quite long, and ripe for a bit of cutting, welding and bending. I would have thought these would be available at a reasonable price from BSA spares dealers. Worth a try, without costing silly money.
Good luck, Dave.