Update!
I wrote to Kenmore support and got a reply. She asked about the thread I was using and suggested using a blue needle with tension of 5 or a polyester thread with the red needle at 4. That should tell if it's the machine or a tension issue. (A poly thread should sew fine at 4 tension).
I'm really happy that they replied to my email! Unfortunately I won't have time this evening or next but I'll play with it on Friday and keep you posted!
Steph