You know it's a bad sign when you have to take the sewing machine apart, and the fabric is still stuck!
After much finagling, trimming and hemming, we have a circle skirt! I'm so glad I tried it out the tutorial at doll size before attempting it in my size. Despite the thread + elastic debacle, I'm pleased with how it turned out!
I'll definitely modify away from sewing directly onto the elastic if I make one for me. Good learning experience about the limitations of either my machine or my expertise. :-)