Tried that, very hard to keep track of. Livesplit wise the easiest would be to use the pause button I think when you end a race and then start next split when you start your next race (gain control of the vehicle) that should also unpause the timer).
But yeah if rules would include the usage of pause button between events, it could also be useful for situations when the game decides to crash (quite frequent on PC).
Edit: Just tested, "next split" button after pausing just unpauses the timer, has to be pressed second time for also split change. Should not be a problem as long as the timer is unpaused at the correct time.
Summary: My suggestion - use Pause button to filter out loading times, possible crashes and everything that is not directly related to racing the event.
I personally dont think getting the highest score counts really as a speedrun. We already have in-game leaderboards for such endeavours and there is currently no good way other than manual calculation if we were to do combo scores (score total of all drift events for example).
Also to reach a specific goal as fast as possible, we would need some kind of in-game notification how many points we currently have. The header "goal" bar is not very helpful and I am not going to calculate mid-race how much 2167*138 makes etc. Monster Truck for example updates pretty slowly - when you combo those jumps on the halfpipe, you need to like break your combo and wait a bit for the game to update your score.
Not all events have laps, so I do not see what is the reason of such a category at the moment? All event progress is calculated in percentages as well.