Adventure 02 works just fine. I noticed that you changed the exit identifiers in 02 versus the others. In 00 and 01, the adjacent exits are lettered identically, so the two letters at each edge are identical. In 02, each letter corresponds to the next card in that direction, so the letters are different at each edge. That method looks a bit strange, but it makes more sense since the order in which the player explores the cards isn't forced like the first two quests.
The system reminds me of Mazescape, a series of puzzle games involving tracing a maze on a sheet that can be folded and unfolded while tracing.