It was probably the position you were in not the reg.
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What was the cracking pressure of the second stage that you were using at the time?
When you were on your back at the surface, you could have done a very simple test to demonstrate whether it was the second stage or first stage that was limiting. While "over-breathing" your reg, you could have tried purging your backup/octo reg. If air came out of the purged reg, then the first stage wasn't limiting.
I suspect that you were hyperventilating. This increased your arterial CO2 levels which increased your respiration rate. When a wave submerged your face in the water, your supine position effectively increased the cracking pressure of the second stage. All of this combined to increase your work of breathing.
It's possible that your reg just needs a little tune-up.
To answer your question, any high end second stage reg can be tuned to have a very high cracking pressure. That could give the diver a false perception of "over-breathing" the reg.
Oops! Yeah. I posted too quickly without double-checking. Huge mistake. I'll fix that. Hyperventilation actually decreases arterial CO2 concentration. Hypoventilation increases PaCO2. My physiology professor would not be happy.By the way there is small flaw in your reasoning I need to point out (I'm an anesthesiologist). When you hyperventilate your CO2 in your blood drops rather than going up. What may happen is when excited you may take rapid shallow breaths that are inefficient and may appear like hyperventilation.
Come to think of it, I wonder if heightened lactic acid build-up (due to strenuous exercise) decreased blood pH enough to cause central and peripheral chemoreceptors to increase the respiratory rate.As a side note, it's possible that your hyperventilation was caused by exceeding your VO2max during exercise.