At the checkpoints, it would be great to see it saved to the advancement logs too.
CP1:
CP2: etc..

Advancement logs? Are you talking about the text displayed on the HUD when you start a race?

And I think it would be more useful to instead list the best time between each checkpoint rather than the cumulative up to each checkpoint. That is, your time from checkpoint 1 to checkpoint 2 might have been really good, but if you messed up before reaching checkpoint 1 it wouldn't be so apparent with a cumulative count.

I didn't mean the best times, i'm talking about each time you do it.
The HUD text is saved to your Advancement logs in Mission and also the mission log of the last mission.
But yes also the best time between could be cool too.