SOLUTION! READ ME: the best stuff for a permanent cheap forever repair:
Get a tube of black urethane roofing cement. the good stuff.
It is really sticking coming out of the tube, and a mess if you start getting it on you. BUT, it dries into a thin, super flexible membrane. PERFECT for those stupid rotting woofers that you just want to work.
Just smear it carfully onto the surface of the surround, as thin as you can do it. Where it is ripped you can even put a thin bit of fabric tape to bridge the gap. let dry for at least two full days. And NEVER worry about those surrounds again.
I am serious. I used it on my Infinitys and it was just what I wanted.