Problem solved! I had bought the new bobbins in a fabric shop while visiting out of town. Last week I went to my familiar LQS, and when I described the problem, the first question was, "Are they Singer brand?" I looked, and found that they were not, but were made by a well-known notions company. I bought a pack of Singer brand metal bobbins, tried them out yesterday, and THEY FIT on the bobbin winder!