I'm not a cryptographer by any means, but it seems like every time you transmit a chunk of video over the network, you could generate a single-use key, encrypt the video with that key, and then encrypt the single-use key with every intended recipient's individual key.
When the recipients get the message, they'd find their encrypted copy of the temporary key in the list, recover the single-use key, then decrypt the video.
That way the only wasted bandwidth is in transmitting keys, which is a lot smaller than video.
The recipients could give the single-use key (that they decrypted with their individual key) to someone who isn't supposed to have it, but that doesn't seem like a problem since they already have the decrypted data and could give that away.
For a small performance improvement, you could re-use the temporary key a few times (for, say, 10 seconds) if the set of intended recipients doesn't change.