You're welcome, everybody. I can't take credit for the technique of reinforcing with nylon thread. I'm sure I read about it on Ravelry. I think it might have been Cat Bordhi who suggested I reinforce the sole by carrying short lengths of the thread across it.
Everybody's welcome to try it!
It occurs to me I should look for a cotton/spandex blend sweater at the thrift store and make summer socks with it.