I have an NPC who "kills himself" when he reaches a target square. That is, he disappears off the screen when he enters his house. For some reason I've never figured out, there is always a delay before he fades out. To mask this, I placed the door on the north side of the house where the NPC is hidden by the house roof when he gets to the door.
With your rat race, I'd try removing the freeze, and placing an NPC Control in the "target reached" event which adds a new "rat 2" (which has zero movement) at the co-ordinates of original "rat 2" and deletes the original "rat 2." You will need globals to track your rats. This would stop the other rat from running when the winner gets to the target. If you haven't done so, make your "we have a winner" sound the first item in the target reached event.
I don't need to tell you that you'll need to mirror this for "rat 1" in case "rat 2" reaches his target first.
If the maze has twists and turns, how do you keep the rats going to the target? I've found that an NPC will often stall if it cannot find a straight line path to the target.
IDEA # II: Script the whole race with two animations which have different winners and let the random choice pick which animation to run. This would permit first one rat to take the lead, and then the other, adding some excitement to the outcome. The race course would be a large stamp animation which overlays on your map. The contestants (rats) could slow down and speed up during the race. You could then have your rats "get lost" in the maze by taking the wrong turn and having to correct themselves.
P.S.: To cut down on work with no detriment to the final result, the first 3/4 of the race animations could be identical with the winner only evident in the last few frames of each animation. If you like the work, you could create additional animations to make the race seem more random in outcome.
P.P.S.: If you're really the wicked one you have claimed to be ( ), you could pre-determine the outcome of the race by checking the player's stats and wager, and weighting the chances of success on how decent a fellow the player is deemed to be.