I don't actually have a way to play the demo, but this is fun
Did someone think about the state of the game in the following way? I'll do an example, maybe it is clearer.
If we start in the "present", then everything has already been affected by the events in the tape. If we examine the drawer with the axe in the present and it says that it is locked, than it is obvious that it hasn't been picked in the tape. On the contrary, if we do not examine it in the present, than it is possible that in the tape it's been picked, so when we actually pick it in the tape, we will find it picked when we return to the present. Perhaps it is possible to alter the events following this reasoning?
I did not follow all the streams and the evolution of the experimentations thus perhaps this has already been discussed.