The Full Racing Transmission isn't really necessary, for starters, so the way you are setting up the gears may be what is causing you ire. Switch back to the stock tranny to simplify things, because the Ram will happily spin up to the top of 4th gear with around 600 horsepower, and use 5th mostly for the draft. I was able to win the race in B-Spec with only about 590 horsepower, Stage 3 weight reduction and Full Customization suspension.
The most important thing to do in the race is to time the overtake in the final lap. It is really important to complete the final pass on the first place car (usually the Toyota, but occasionally the Silverado) right at the end of the back straight, because the AI won't quite have enough oomph to catch back up to you coming out of the corner and pass you before you get to the finish line (the Silverado does, but it is rarely in the lead by the end of the race, and whether it can actually get by you is another story entirely anyways).