I discovered the REAL cause of my thread breaking and skipped stitches. One of the sensors for the stitch length regulator was making poor contact with the carriage wheel. When moving in one direction the sensor would not immediately turn, so there was a slight delay between moving the carriage and the stitches. That caused the extra stress on the needle. The thicker needle helped, but the final cure was adjusting the sensor to get good contact.
Thanks everyone for all of the other ideas. I believe it's important to get all of the factors mentioned correct. I quited a queen size quilt over the weekend, and I could tell when something was not adjusted correctly, such as the height of the take-up bar, the top/bottom layer tension, foot pressure, thread tension, etc.