Well.. I don't have any idea about how the replays get saved. All I know is that it's very glitchy. I think it stores the position of the body parts and which joints are contracted or extended and in which frames those things happen (judging by the glitched replays).
I think that it would work better if the replay file stored only the "joints information" of each player and the key frame number (the frame the player can interact) in which the movement started, since everytime we start a replay the dummies are "reset" to their initial stances.
Of course the file will need a header to keep the additional info, like the version of the game, the name of the players, the total number of frames, the number of frames per turn, and maybe even the date when it was saved.
This is how an emulator movie file works, and I think this should work for Toribash too.