The way I would imagine that would be better than to have puzzles that can be switched from a real puzzle to a "trap" puzzle. A trap puzzle would be a red herring especially designed for people who did the original puzzle.
For example, in the the original puzzle you have to find blue stones that arrange to a specific pattern that correspond to a code. The trap version would be a few completely irrelevant blue stones that would be unlikely to grab attention to the people who didn't do the first puzzle. For example they could be used as dead weight for a scale-based puzzle or as rubbish the players has to look through in order to find the real clue.
The idea loosely comes from Danganronpa. An kinda escape room-like video game. The sequels tend to play with players expectations, sometimes confirming them, sometimes to turn them against the player.
Edit: I realize it is much easier said than done. However, non-replayability looks like such a big problem that I guess that it could be worth making a lot of extra effort.