It sounds to me like you are doing well, and making good judgement calls. I'd wait on going to the dog park with the pinch. I would continue to walk him around your neighbourhood until he is more relaxed and responsive to you.
I'm a bit confused about the sizing and fit of the prong. You said that one of the two collars you tried on him fell down to his shoulders, so you went with the looser one? Did you mean the smaller, tighter one? It should be snug enough that it does not slip down.