Dear WW: Birds have a very interesting lung arrangement. The lung has to be very small, and very
effici;ent to avoid needless weight. When the bird breathes, the air goes all the way through the lung,
and into a thing like a condom, so that exchange is maximized. In mammals, only the upper portion gets
changed until maximum O2 intake is required by exertion, etc.
As you may have noticed, birds have very tiny nostrils, and must have to be mouth breathers, though
I do not know how to confirm this. A dog's panting is mostly a heat losing mechanism. Birds like your
trapped struggling one might need to lose heat, just as a dog would, and so overbreathe.

I once had some fun with the pharmacology prof. He was getting a bit senile, and not keeping up his reading of advances in physiology. He showed us an experiment that he thought proved a new drug stimulated
respiration in a cat. I challenged him to have cat breathe through the same apparatus without any drug.
He did, and the tracing was identical to the one with drug. He asked me to explain that. I said: "Your apparatus increases the physiological dead space." Same reason you can't hide underwater while breathing
through a three foot length of hose. I still laugh remembering movies showing someone hiding under water
while breathing through a straw. Can't be done, not enough exchange, tidal air way too low.