yup local here. I did a rough draft of the essays, probably will amend them from time to time as I wait for the rec letters. Other than that, have done rest of the application. You?
I have a friend who once sought rec letters from a prof who taught him and a prof who is the head of the sch. The prof who taught him was able to give him a testimony based on his results and performance in the course while the prof who is the head told my friend to look for other profs, since this prof has never taught him before and couldn't write anything personal.
I think the requirement just meant any profs, but you would want someone who could say something about your ability!