Compression over the carotid sinus can cause a vagal response which would drop the heart rate and blood pressure (think about fainting soldiers on parade with tight collars). In this case, during the immediate recovery period, the opening pressure would potentially be lower and a swift opening might well reduce the arterial spray.
I'm not convinced the airway would have that much blood around it from where the cuts were made. The only bleeding at the front of the neck would be from skin and fat blood vessels and the massive bleeding from the carotid arteries would be draining away from the severed trachea. The lack of blood on the victims front is why the doctors felt the cuts were whilst lying down.