I'm going against the grain here but I would have worked the pt as the OP did...and to be honest, I don't see how/why some of the people that posted in this topic are in EMS. We are here to HELP people, so do it, even if you think the outcome is poor, there still is a chance. I really hope some of you don't work on my family. They aren't dead until they are warm and dead.
I suggest you take a course of study that will take you through a basic biomechanics course, because it'll give you an appreciation for understanding what happens to the body when certain forces act upon it. Only then should you take PHTLS, which by then should be very easy for you to comprehend. That's when you'll have that "lightbulb" moment about traumatic arrest.
Some of us in this forum have very advanced training and education in this field. Primarily, those people are those of us that have physician – level, athletic trainer – level, physical therapist – level, or similar level training on top of being paramedics for other advanced prehospital provider above EMT.
I have met several people that are both athletic trainers and paramedics. Because of their education in sports medicine and paramedics, I think you would find that those people in particular would be extremely good at evaluating traumatic injury. They also know the forces involved, where to look for injury because of those forces, and also have a very good understanding of when it is not likely that someone would survive their injuries.
In my own educational background, I have received extensive experience dealing with collision, contact, and noncontact sport injuries. Most of my time has been spent dealing with football, wrestling, soccer, volleyball, baseball/softball, Track & Field, swimming, diving, and basketball. Although I have never worked a Rodeo, I feel very confident in my ability to manage injury sustained by the participants of that Rodeo. This is because the education that I have received over the years would allow me to properly identify and treat those injuries. I am also very well acquainted with the fact that some injuries are not survivable, even if I had a full trauma team on-site at the moment of injury and ready to go to perform life-saving surgery, even assuming that they knew exactly what the injury was going to be.
That is why when I read the scenario posted by the OP, I responded exactly the way I did. That is probably also very much the reason why other posters on this particular thread said the same thing. Now, it is completely obvious that most of the people here on this forum do not have the same level of training that I do. Some of the people in this forum have much greater training than I do. I would, at this point, wager that a fair number of people here have more recent experience than I do. When they say something, I generally listen and determine if it applies. You should too.