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The difference in the standings between points and times can be quite significant and is expected. When using points, the number resolution is to a whole number, where as scoring by times yields a scoring resolution down to 0.001 or better.

Point scoring cannot differentiate to the fine degree that times scoring can, so standings can be quite different between the two scoring methods. If you have a timer, using times scoring is far more accurate in determining the fastest cars.

No, you cannot override the standings without first changing the race results, which is not recommended.

You can write down the results, factoring in the tiebreakers, and use that list to announce the winners instead of using the Standings screen.