I cycle at the higher end of my aerobic threshold to get around and my bike is single speed so I have to go anaerobic on hills. Do you cycle at a more leisurely pace or do you maintain constant nose breathing even during strenuous exercise? If the latter, I would probably caution you of the health effects of that too.
I'm definitely curious if you have references to negative health effects of nasal breathing. I've seen quite a bit on the positives, even with strenuous exercise. I maintain nasal breathing when riding fast, during kettlebell workouts, and sandbag workouts.