Most people use paracord, because it tends to be the toughest thing that they carry in quantity. Boot laces can be used in an emergency. Your sash cord, if I am visualising the right stuff, should have been plenty strong enough.
It is just possible that technique plays a part in how fast the cord wears. I think I would get some paracord, or more sash cord if that is what you carry, then practicing with that. As a fire lighting method this is something that one should be able to improvise, if you need to carry a special cord you might as well carry a fero rod, or lighter.
Mr Mears sings the praises of a rawhide cord as being better even than the pull cord for starting petrol motors. I tried making a rawhide cord, but got the technique wrong, it broke

and I haven't had any more rawhide to play with,
Ash might not be the easiest thing to start with. I haven't tried it, but would think that it would be harder work than sycamore, hazel, elder, birch, ivy or cedar, and hence harder on cordage.