Lord Grievous said:

I noticed that all but your AVCHD version of ANH has 24p and the rest at 23.976p, could this be the problem?

EDIT: The sample plays fine on my PC, but VLC says that it has a frame rate of 48 whereas all my other HD videos have either 24 or 23.967. Could this be why it's sped up?

The frame-rate of all the AVCHDs shows up doubled in VLC. Don't ask me why. Tsmuxer gives the correct frame rate - check if you want - so that's not the problem.

23.976 fps is more compatible, so the only AVCHD you might expect problems with is indeed the 24 fps ANH:R. I don't know what to suggest. You could try converting the m2ts to an mkv, if your TV supports those (does it act like a media player?). I don't know how to do this as I have never done it this way before (most people want to go the other way), but I believe therer are ways to do this. You might try MakeMKV.

edit - I see Satanika beat me to suggesting making an mkv. :-)