I'm very familiar with Greg and his ministry. I have found his teaching to be very sound. You are right that he doesn't come from the institutions that you would hold in high esteem and that he is friendly to the types that you and I would both oppose. If you look closely enough at his teachings you would find a few small things to take issue with (well, I call them small, but can't speak for you).

This article on "Experiencing God" is right on the mark.

Note that he is primarily an apologist, not a theologian. But I haven't found anything in him that tones down my support and respect for him.
Please read his article on EG and let me know what you think.