I was creating time trials for each character in Sonic R, and after many attempts I realized something strange about the default time trial times on a new save. They are too low to be overwritten by actual times when racing on certain courses with certain characters. For example, in Radiant Emerald, the fastest lap times you can actually get inbound as Amy, Eggman, and Egg Robo are all above 1:00:00, the default Lap Record, at around 1:14:00, 1:02:00, and 1:12:00 respectively. This causes issues with the Course Record as well, as it is set at 3:00:00, and when adding the lap times together, naturally, it exceeds this.
As an interesting side note, the Sega Saturn version of the game, released before the first windows version, does not have this issue, as it sets the default times higher. The default Lap Record in the Saturn version is 1:20:00, and the default Course Record is 4:30:00. Here's to hoping someone here knows how to fix this.