i don't do a mash out at home, because with my electric burner it's impossible to regulate temperature.
when i do it at my friends pad, i heat and stir for 5-10 minutes until temp is reached. i usually stop 2 degrees short because it will continue to heat a bit after the burner is off.
really, you can do it either way.
if you're having trouble reaching FG, you may be mashing too high. are you using a floating thermometer? what are you mash temps? i usually stay around 152°F.
using the pot for heating can be rather inconsistent and you need to stir a lot to make sure you are at the right temp. hope you figure this out.