Just ran this last night in the Honda Integra Type R (it has a better power-to-weight ratio than the Acura Integra, plus it's cheaper).
I modded it with:
Full Customize Suspension
Sports Brakes
Brake Balance Controller
Computer
Turbo 1
Racing Tranny
Racing Flywheel
Triple Plate Clutch
T2 Tires
Lightweight 2
Which turns out to be 263hp, and a 4.4 power-to-weight ratio (exactly the same as the Spoon Civic which you'll win) My front tires were a healthy yellow by the end, and the rear tires were still blue.
It was a good challenge against the Spoon Civic and the Beetle Cup car, except that the Civic pits on lap ten every damn time, what a waste. (The Beetle Cup car didn't pit) Until lap ten though, we were never more than about 3.xxx apart. Deep Forest was by far the hardest race. Just remember to go easy on the gas through the corners and don't be afraid to let the back end swing a little bit on the long off-camber left between the two tunnels, it's much easier to keep your speed up that way.