I think you will be fine, RDWHAHB!
You don't have to stir constantly once the malt extract has been dissolved, just once in a while so that the kettle bottom doesn't scorch.Cooling the wort as fast as possible is always a good idea, but if you can't do it in 10min it doesn't mean the beer will suffer. I actually don't have a lid for my 10gal pot, I don't think you even need one. Most brewers choose to remove the lid during cooling. The evaporation from the wort can cause condensation on the lid, that can drip back into the wort and create a vegetal aroma.