Your not going to effectively monitor vitals in a patient that is thrashing wildly on the cot, face down. Do you think your pulse oximetry probe or etCO2 is going to stay in place? Perhaps some electrodes, you'll see the tachycardia and artifact until he brady's down and dies on you. You decide to transport someone face down on a cot, in restraints and they die, you will be owned. There is enough literature warning cops, and hopefully EMS professionals of the very real danger of transporting patients in restraints while prone.
Take a fat patient and lie them on their stomach and see how well they breathe. Now roll around and fight with them, raise their temp, hr, bp and mvo2. Now place them prone. See what I mean? Bad idea, and completely different than lying supine on a board.
I have been in this situation, not heard about or read about, but running the call. The patient fought and fought with the cops until he didn't, and at that point it was all done. He had immediate resuscitation and stayed very dead. Sure, the drugs and agitation added to it, but I would bet his chances were better if he were not face down. I carry a cuff key on me at all times. If the cops cuff them, they come, and under no circumstances will they be transported in the prone position.
Off my soapbox.