I must say that of all the jurisdictions I've had to interact with around here, the Park Police are the most reasonable if you are respectful and explain to them what you're doing.
I think the park police in general have a pretty low-stress job for law enforcement, so they don't arrive on scene with their panties in a wad even before you interact with them. They must be very well-trained for interacting with the public, particularly with tourists. So if they can put up with the ravening hordes of high school senior trippers, they're more than willing to take five minutes and talk to a large-format photographer.