I still think these beheadings are not actually being recorded live.

That's why these guys are cooperating reading the messages. They were probably told to record this crap but that they wouldn't actually be beheaded if the US changed course. So they go through the motions, read the statement, and you see the knife being taken to their throats, but don't ever see anything really being cut.

Then they probably behead the guy off-camera with a big axe or something, and then place the dead body on camera.

There is no reason why these terrorists are cutting out the gore of these guys' throats being cut, as that would actually make the most impact (including their screams as it's starting to happen).

It is even possible that these messages were all recorded in a short period of time before anyone had actually died.