When my sew-up or clincher tire's casings develop a weak spot (bulge)
that threatens to explode when inflated, I have used (as a "boot" on
the inside) those thin, cloth self adhesive "security badges" that some
companies require their visitors to wear. However, some companies do not
allow you to take them; I'm sure there are other sources of the same
self-sticking cloth labels.
The great thing is that they are self adhesive, strong, very thin and
don't add to the bulge.
Art Yow
San Francisco