There was a tree similar to that in Deusen Park in Houston that I drove past every morning on the way to work... tempted to sneak in one night and "find" a few of the "knots".... talk to the park admins and put in dibs if they decide to take it down.
Mike, go ahead and cut them down, and then submit the bill for doing so. You can claim that they were a hazard, and that you were afraid that a piece or the whole tree might fall on somebody, causing injury claims against the park. You never know, you just might get away with it. Personally, I doubt it, but it's at least worth a try.