The reason why they tell you to start chest compressions when the breathing stops even if you think you feel a pulse is that it is really easy to feel your own pulse, especially in such a high pressure situation. If the electric circuitry of the heart is still intact you wont damage it, but if you skipped compression because you felt your pulse that person is very dead.

On what is so hard with putting the cell phone on speaker and setting it down next to the downed person? Your are still on the line but have your hands free?

Aside from that: thanks for helping a fellow human and congratulations on keeping it together under high pressure.