It's my understanding that anything other than tourist snapshots are clearly proscribed there, to protect local photographers/videographers and the income the palace makes from selling souvenir postcards. It's the same reason why you can't take photos of the Emerald Buddha - not for religious reasons, but so they can sell you postcards. I wouldn't even try it - the Thai authorities can be pretty strict and unforgiving about these kinds of things, and on a matter such as this, a little (or a lot) of palm-grease wouldn't solve the problem either, once you've gotten into it.