Good answer.
In all seriousness - the park is large and has a multitude of uses, and given that I intend to play low key / instrumental music (without thumping bass or loud percussion) I am fairly confident I could get away with it. If I wanted to get more people and make more noise I'm pretty sure I could get permission.
It's a wonderful park in the summer, people of every age and every walk of life do a hundred different things there. Bringing acoustic instruments to the park itself for performance is another idea, but 1. it's hard to wheel a piano onto a grassy hill and 2. it would be kind of neat to do a surround setup at some point.