So, thanks to this thread, I made a valuable piece of self discovery this morning. I cleared the right to the right, as described above. Then, as I was setting up for the left, I realized that I also clear the left nostril to my right! I've never thought about it before!
When I do my left, I keep my left arm on the bars, hold my right nostril with my right hand, and then still shoot right, sorta under my raised right elbow. I think I do this so I'm never looking left, which can lead to going left, which can lead to becoming a bloody smear on a semi.
Thanks, Xiyangshen, for helping me better understand my riding habits. I'm forever in your debt.