In this game, you are going to use a completely different method for breaking champion difficulty than last year's game. During this career, you can ignore the Shootout, Daytona Duels, and All-Star race as they are non-points races. Go ahead and start up a career and use the following as your settings:
Race Length: 20 or 30%
Tire Wear: x4
Fuel Mileage: x4
With these settings, you can go ahead and get started. The basis of what you are going to be doing is starting the race without bothering to qualify. Then, park your car right away as the field circles around. Your goal is to back up into the field and try to DNF as many cars as possible. As long as the field hits you in the side or rear, your car will not break but theirs will. After every hard crash, a few cars will be taken out and you will move up the field.
As you begin to get a few laps down, it may take you additional laps before it counts you as passing the DNF cars. Also, if you get a flat tire or your engine wear starts becoming critical, pit during the red flag and repair your damage. Keep those two things in mind as you progress in the race. Once you are happy with your position, go ahead and crash yourself head on into another surviving car and it will end you in your current position.
During the season, there are four tracks you want to watch out for, as wrecking the field will bore you to death. These tracks are Bristol, Martinsville, Sonoma, and Watkins Glen. I personally recommend you simulate these races during the career unless you are decent at the game and can muster a strong finish in a 2-5% long race. Use this sparingly! If you simulate too much, you could force yourself to start over from falling outside of the top 10 in points.
Another thing to look out for is glitches (who would have guessed). There are a lot of times where the game will just give you whatever finish they want, and if that happens, remember you can restart a race at any time (even when it is complete) until you get a desired finish. The second type of glitch could actually work in your favor! Occasionally, you will see a checkered flag wave right before a red flag, even if the race is no where near complete. If this happens, you are either going to restart by yourself thanks to the glitch, or with the pack. Either way, the glitch forces the race to end in 2 laps regardless. Therefore, it is best to finish up by yourself and enjoy your free win, or restart if the latter happens and you won't be pleased with your finish.
Last thing to worry about is the chase. Once you make it in, it is in your best interest to write down the drivers in the chase and paint a virtual target on them. There is a big chance you entered the chase with 0 wins (I only had 1 but it was because of the aforementioned glitch), so it is important to take out those competing against you. Personally, I made it my sole goal to continue crashing the field until all 11 other chase drivers were trashed, and then finished ahead of them. That way, no matter what, I was earning more points than them and retaining my points lead. You have to either simulate Martinsville or settle with a bad finish during the chase, please keep that in mind.
As a closing note, always make sure your finish is correct before you advance after a race. If you get critically damaged yourself (it happens often) or you aren't happy with the result, restart restart and restart. There is no penalty to doing this, and once you advance, you can't go back to a race.
Big thanks to bongohawley for initially discovering the method.