So, I may be old fashioned but, old racing games back on PlayStation, Nintendo etc. If you did more than one race, your best time would be recorded by a transparent, non-collide ghost. And it would be reset if you beat your best time.
Well, personally, I think that'll be pretty cool to implement into the game however, I think it should only be if you're in a game on your own as it may be mistaken as another player.
Just a little idea rattling around my head, let me know what you think