Our first grey was extremely timid and obedience classes would have overwhelmed her and been a nightmare. It took her 4 years to go outside on her own, and that was only because she discovered rabbit poop. When we first took her to a greyhound playgroup, she stood and trembled. But week after week, she got more and more comfortable. We took her to Dewey and the first year she spent upstairs in the condo. The following year she came down for food and would occasionally lay on a pillow with the other greys. Baby steps all the way.
We also have a large farmers' market in town. My dh would take her every Thursday when it was less busy, and gradually she would walk around and feel more and more comfortable. She was never 100% comfortable unless she was at home, but gradually she improved. We were always on alert though; one neighbour put up windchimes and we knew that would scare her so we were always encouraging her in a happy voice upbeat manner. That's what I mean about being alert...anticipating what would scare her and catching it before it terrified her.
I found that I got good at determining what would terrify her and remove her from the situation, and what would be uncomfortable for her and help her through it. We managed what was comfortable for her, whether it was our preference or not. I do this with Brooke too. If Brooke doesn't want to meet people, I don't force her, rather we wait until she goes up to them on her own. The trick is finding balance though between facing uncomfortable situations and getting through them vs terrifying situations that she never would get desensitized to.
Going for walks with other greys helped too. And adding a second grey was the best for a number of different reasons.
This probably doesn't help much, but good luck!