No permits needed.
The regulations apply to special events (think Papal Mass) and professional film companies. No one's going to roust a dozen photographers shooting big weird cameras, unless we/they make a nuisance. Then someone will (rightly) send in the park rangers and tell them/us to move on.
Originally Posted by Superuj
The birders routinely congregate in the Rambles with tripods, without permits. I've shot on tripod in Central Park for years, and no one has ever once questioned me.