As long as you can keep up with the pack, you should be able to win by cheating.
On Indy Road Course, brake at the driving line's indication, and start turning right, right away, cut that first corner. That will make up a lot of time.
On Nurb 24hr, you can cut the grass and skip that HUUUGGGEEE chicane, that makes up about 3-4 seconds a lap.
On La Sarthe, you can cut the 2nd chicane and gain about a second a lap.
And like slump said, keep an eye on the names in 1st & 2nd in points. Push them off the track, just enough for them to lose 4-5 positions, that's all it takes for a 30-50 point swing in the standings.
Another tip, is don't race the computer. Just play 'follow the leader' and only pass in a straight section by using the draft. You have 20 laps, you only have to pass 1 car per lap. You don't need to be in the lead by turn 1, there's no point in over pushing the car.
Try to get to second place, and hten just follow the leader until there's 2 laps to go. Then try to take the lead and get 1st. If you succeed, 1st. If you can't do it, then just take 2nd. Big picture racing means you have to focus on overall points for the full 6 race series.
On one of the coursed where it rains... Suzuka I believe (where you can also cut the last chicane again) they all pit on lap 1 to swap to different tires. That gives you about a 30 second head start, then you just gotta keep it clean.
It's better to slow down too much and lose 2-3 tenths, than to try and force it, spin out and lose 2-3 seconds. Big Picture racing.
Good luck.