I would let him do free flowing writing at home, while he is working with you- after all this will build his creativity. Maybe he is simply too young to be learning about the whole writing process? Maybe it will eventually come and become easier as he writes more and more? In my DD school (fourth grade), beside the long writing assignments (never heard about the four square method though)they do Daily Obligatory Tasks (DOT's) at the beginning of each lesson, and in LA it is usually one paragraf on an assigned topic. One day you are going to like the topic, one day you will hate it, but I think it gets them going and being used to writing about variety of things.
I am all for creative writing, so just learn how to survive this teacher. Maybe later on they won't be nagging him about mapping the whole process (I understand that the whole district uses it, but maybe if later on his written assignmnets are good and clear, they won't bug him about mapping it down). I keep telling myself and my kids that grades are not the most important thing here, the most important think about writing is to write clearly and easily. Besides, writing is such a subjective matter. You will never satisy all your readers :-)
Ania