First of all, I don't really think it is the batting that is causing the problem.
When you are heading away from yourself with the stitching, you are creating something which is abnormal to the machine. This is with the assumption your thread goes thru the needle, front to back. So it does that, and then with the movement you are creating you now in effect have it "s'ing" back in the other direction, and that could easily cause the break.
You might solve the problem by slowing down your speed in moving the quilt, but I almost doubt it. While you said the tension looks good, you might want to adjust it. Sometimes you can adjust it, and it makes little difference to the visual, and yet just seems to make things work better.
Another possibility might be to try a different needle such as an embroidery. I'm not too familiar with your thread type, as to whether it might be one that breaks easier? So you could always try a different thread.
Good Luck!