Hi
I'm no instructor, but FWIW, my mantra for PFL's is this : glide, trouble, field, trouble, mayday, pax brief, shutdown.
For the trouble checks I was taught FCMIT - fuel (confirm on and change tanks, primer locked), carb heat, mixture, ignition (confirm on and switch between each mag), throttle. I wouldn't do my mayday call first, as ideally it would be nice to fix the problem, and using the old saying, AVIATE, NAVIGATE, COMMUNICATE it should be well down the list. That being said, with a bit of altitude you are more likely to have the call heard by someone than closer to the ground so best not to leave until the absolute last minute, unless necessary. Maybe others have some thoughts also?
Nev