I was in the same boat as you. I am from a non APA school and was interviewed at 4 APA sites and 4 non APA and matched at an APA internship this year. I would suggest that if you want an APA site to think about expanding the geographic search. Also, look over the statistics for the last couple years of the internships you would like to go to and see if they have taken non APA person in the past. I also emailed DCT's of places that I thought fit with my training goals and asked if they would accept my application (two sites said they would and I got an interview them both). I also did not apply to highly competitive APA sites, 150 applications at the site was my max, most of the places I applied to had less than 100 applications. In the end it is about how you will fit with what they offer and what you will offer them in return. It is a tough process and even tougher when you don't come from an APA program. Hope this helps.