Thanks to everyone who wrote to encourage me to keep trying with nylon thread. I had previously experienced constant problems with the thread breaking. I've changed two things, so I don't know which one made the difference:
- On advice from someone in this group, I switched to a smaller needle--am having success with a Schmetz size 10. (Had tried a 12 before.)
- I noted that Harriet Hargraves recommends putting the nylon thread on the table, near the machine, taping safety pins to the machine and running the thread through them. It occured to me that my Juki has a support rod you can pull way up, with two loops in it, to use when one is threading the bobbin. I decided to put the nylon thread right in the usual spot for thread, and to run the thread up through both of those loops before threading the needle. This gives the same effect-- the thread goes straight up, so doesn't tangle.
Whichever is working, or maybe both, I find this a winning combination, and am now having no problems at all. It even seems to look better--not so shiny, but I have ordered the Sew-Art International thread HH recommends, in smoke, to see if I like that even better. Thanks to everyone who answered my plea.