I don't think a steeper penalty would fix anything.
If you are trying for points, and willing to game the system, then they can just pick one of the "A & B are C & D" clues. Make a guess, and check errors. If it is wrong, then just throw the puzzle away and grab another. If it is right, then you just got a huge unfair advantage.
Even if the check errors button was gone completely, people could still use the guess method to get best times. Some puzzles would go badly early, and they would be unsolvable, but for others they would get record times. The main players that would be hurt are those who don't care about points, and just used the "check errors" button to make sure they weren't off track.