well - I had the exact opposite situation. My GF and I have 2 basenji's (she has introduced them - Sophie and Stick)
Both are rescues. Sophie had that exact same set of issues at the dog park. The first time we brought her there she growled for 2 hours straight. She had no socialization. We kept bringing her there and trying. Things slowly got better. These days she wanders around on her own and sometimes plays.
It took at least 6 months of going before she really played. One important thing was that we watched her very carefully and tried to manage her anger level. If she got to worked up he made sure to defuse the situation. Very quickly, we learned what the difference between her growl and her "Hell-Bitch" growl. These days she growls when playing, so it is a part of her personality.
At the same time we were bringing a known dog into our home (or going over to his home) in order for Sophie to get some interaction time that was not so intense.
the comment about it being defensive behavior aligns with our experience. She was most growly when she was close to one of us. As she developed she would start to wander away from us and interact with other dogs. When she got overwhelmed she would retreat to the legs of the nearest person (she always liked interact with the people) and once pressed against some random stranger she would get growly. Def defensive.
Once we helped her develop to a point where she could kinda interact like a normal dog, we got Stick so she cold have a pack. She is still a bitch, don't get me wrong. But she has come so far.
I don't know your dog, I just wanted to show that it is possible to get them to be more social if they aren't inclined to be.