Update #2: Ignore everything here, there is no emulation problem and that explanation is incorrect. The speed boost happens when you are out of bounds and press up when a dark blue car is on screen, for whatever reason.

Update: I have figured it out. It is not an emulation issue. For some reason, when the timer reaches zero, you can push up again and will gain an extra speed boost resulting in a time of 2:59. Without the speed boost, 3:06 appears to be the best possible time. In the case of my rejected run, I held up throughout the entire run and it gave me the boost.

So my run was just rejected by NESCardinality because the car started going faster than normal after the timer reached 0. I didn't notice this whilst playing or looking at the video afterwards, but I was confused as to how times were different because the run is the same every time unless you get rammed somewhere.

This video also has a speed up when the timer reaches 0:

Can someone try and reproduce this on NES? I have no idea why this is happening.

It's fine, honestly. If it wasn't rejected I doubt I would have ever discovered the boost. It is a weird run to verify, it looks as though the speed fluctuates randomly. The other run that was removed definitely needs to be looked at again though, because 2:53 is definitely achievable.

Thanks again for getting back to me so soon, PMYA. I'm glad that it was resolved so quickly, and that you were able to figure out what happened and improve your run in the process.

I've re-verified dadabeep's run. It's very strange that the sound effect the tire-shredders make in his run is higher pitched than normal, but everything else seems to suggest that the run is legitimate. I can only guess that the sound effect is perhaps an emulation anomaly, and it's rare to hear that in a single sound effect of an NES game. (I have perfect pitch so details like that tend to stand out.)

Sorry I couldn't fix everything during that very long stream. I'm glad we were able to talk in real time and that the resolution led to further improvement. I hope you'll keep trying to gain those 2 extra seconds!