Looks like the only explanation is she got her head hung up in the feed chute somehow, and the coyotes decided a free buffet was not to be turned down. Possibly it's low on feed and she was trying to get the last bits?

Our distinct impression was the doe got her nose stuck and somehow cut off her airway. It was very difficult to dislodge head and nose from the protein feeder. We had the same brand feeder.

I have seen this before on this brand bulk feeder and a couple of others. The issue is the baffle just inside the chute to prevent rain from blowing in and the deer get their nose/upper jaw hung up on it and they shut off the airway like another poster said. Coyotes didn't kill her.. What a horrible way to die.
One of the reasons I don't care for single chute bulk feeders. I saw a young Axis buck with very short antlers get his head hung the same way. I prefer feeders with large troughs for this reason.