Hey Matt, I have a very high opinion of biblical counseling -- it was a pastoral counselor that I saw in my darkest moments. I don't necessarily have the answers for how to reconcile Biblical counseling with psychology, but it can be done.
I don't know if we can see sin as the primary cause for suffering -- look at Job. With the NT I try to be cautious of trying to make judgments of who does or does not to suffer, but in my personal struggles with mental health I find a lot of solace in that my struggles bring me closer to God and make me recognize my need for Him. Traditional psychology is more limited, in my opinion.