Hi mpaguy,
From what I was told, schools look for around 4.5 AWA. I don't think a 4 is low enough to raise any red flags. I think they look at the AWA to see if you were the one who really wrote your essays/personal statements for your application. Some people get their essays over-edited to the point where it isn't theirs anymore, and they just want to make sure that you were the one who wrote them.
As for your stats, congrats on a good GMAT score and a great GPA.
For comparison, I also scored a 710 on the GMAT and had a GPA of 3.4 UG BA in Economics. I just applied for programs this year. I too, as stated above, am not an accounting UG major so I applied only to schools that either had programs tailored to non-accounting majors or accepted them. After some research, I decided to apply to USC, UTA, Wake Forest, ASU, Baruch, and University of Houston. So far I have been accepted to USC, UTA, and Wake Forest. I have already committed to going to USC, so the rest of the schools don't really matter to me.
Another top program that is tailored to non-accounting majors is UNC Chapel Hill. I decided not to apply there though because they require 3 letters of rec, and I could only comfortably get 2.
USC, UTA, and UNC do not need you to take any accounting classes. USC has a summer intensive program to catch you up. Wake Forest, ASU, University of Houston, and Baruch will have you complete their prerequisites before you come in, but they are willing to accept you even if you have not taken any accounting courses. I don't know if you want to apply to ASU because they give priority to Finance and/or Accounting majors.
Hope this answers your question and gives you a good idea where you stand. Best of luck on your applications.