is the logic 100% correct on parachute? you can still move the boat after game over (although for no reason) and it seems to take several presses of 'time' to get back to the demo mode?
I believe that is correct as the physical game is behaving in the same way. I can't verify it right now but if I'm not mistaken it's also possible to move the player in Fire when the game has finished. Perhaps this is a bug in the original ROMs?