My money's on master cylinder..
So is mine TBH. Cant see how air would affect the distance travelled in this way - surely it would be the same all the time. Nor can I see it being the servo - if that failed surely the brakes would be harder not softer. And if it was a balance valve issue would the car stop straight as it does?
Howard i read all of the previous and suspect your friend has looked down these avenues, where i would be looking is at the shoes themselves, if the head of the shoe where it sits against the piston of the cylinder is worn down, x that by 4 on one hub then x2 for both rear hubs that is a lot of travel for those small pistons to move before they hit the shoe head, this was notorious in the 80s when Brake manufactures were cutting costs by asking you to part ex brake shoes so they only had to replace the lining, the metal part didnt get replaced, i spent many a time having to put a dollop of weld on the end of each shoe then refile, this will push back the pistons into the cyclinders and give a good stroke first time.