Sorry for the double post, sometimes my thinking is a bit slow, but...........just an additional thought or two.
The best way to find some of the old flat frog hair(IMPO) would be to check out small mom and pop shops in your area and keep an eye out on the web. Another thought is to check out local archery shopsI, i think the flat rubber has been used on hunting bows. I hate to say this, but if you find it buy all you can, I have looked for hours on the web for it to no avail, and the small shops are getting fewer and fewer.
Good luck and God bless, boxcar