I can't remember if you answered already, but are you using a hopping/embroidery/FMQ foot? The kind with the circle or C shape at the bottom?
Are your feed dogs down? Up? I do it with mine down, but I know Leah Day leaves hers up and you can cover them with a note card.
Is your quilt well supported around the machine so that it's not catching on the corners of the machine?
When you're not FMQ and just piecing normally, do you have issues with the thread skipping at all? I ask because I just bought a cheap Singer to use downstairs when I'm with the baby and toddler, and I'll be returning it because when I piece with it, it skips stitches randomly and the thread will wrap around the needle and jam. That's even with a new needle, Aurifil, and straight stitching.
How did you baste your quilt? I know many others have had success with spray basting, but I must use too much because I always have problems whenever I do it - even if I iron the sandwich before quilting. The thread always breaks, gets wrapped around the needle, jams, skipped stitches, you name it and I've had it!