Ok, problem solved. I got a Firefox add-on called "Flash and Video Download v. 1.2.1", and it works fine. I'm saving to .flv files and using VLC to play.
Where Leviathan can, it will. The state, by its nature, always prefers security to liberty. Lately, technology has offered it means it can't resist, means of mass surveillance that Orwell would have been amazed by. The process is inexorable – unless it's resisted. Obviously, we need protection from terrorism, but not at any cost. - Ian McEwen