I always laugh when dispatch says that; my part time job has a couple of dispatchers who work as EMT-B's with us, and they now dispatch it as Unconscious AND breathing, just because they hear other dispatchers say that and see us all laugh about it.
A new protocol we got for Altitude sickness states that the best way to treat it is to (Paraphrasing it) "dress the patient modestly": protocol states "decent the patient" Not DESCENT. I typed the sentence into Word, and Word Grammar went 'Uh Uh wrong word choice' So I don't know who decided to type up the protocol, but they are goofballs.
You did a good job covered all the basics and realized that you're 5 min from a Level 1.
One thing I've seen sometimes overlooked by crews that hand off Trauma MVA Pts is failing to document the Mechanism of Injury, (i.e. Location of Pt in Vehicle, Speed of Vehicle, Type of Impact, Rollover/Head-On, Seatbelted Y/N, Ejection Y/N, Helmet Y/N etc). In a Non-Airbaged Vehicles - Look for Steering Wheel Deformity/Signs of Impact, Signs of Windshield Impacts etc.
Did the Initial BLS Team Auscultate Lung Sounds? With Agonal Breathing I'd reassess for Flail Chest, look for JVD/Tension Pneumothorax/Hemo. etc.