It may be possible by using sector timing. It won't be feature rich though with reaction time etc.
If a sector could be placed at 60ft, 330ft, 1/8th mile and 1/4mile theoretically you could do a single player run to the end.
You could then quit back to the track menu, watch your replay and go to the sector timing screen to see all the numbers at once.
I tell you what, i'll have a crack at making it in another couple of hours when I get on.
Edit: It's looking impossible. Sector times seem to be only after a large corner, or there is something I haven't figured out yet.