The collision penalties seem to only kick in when you pass a certain threshold or involve the front half of your car.
Play with some other FR cars, use a manual and memorize the AI's movements. The AI cars always take the same paths so you can easily predict if you have it the first time out of Chicago.
As best I can remember:
1.) Brake late on the first turn and gently slide the your back half into the first car. There's your first pass, maybe the second also.
2.) Cut in between the next one or two cars on the way to Chicago. Take the turn on the inside and there's another pass.
3.) Feather it and get straight-line acceleration out. This spot is where you might get passed from the left but you can gently maintain contact with them and it gives a weird assistance.
4.) Draft up to Hammerhead.
5.) Brake late into Hammerhead. There's some cones you can run down and actually cut across part of the corner earning you some passes. Otherwise, gently use the other cars to physically brake your way around the turn.
6.) Again, keep it clean on the exit and don't acceleration until you're straight.
7.) Don't go flat out on the Follow-through. Downshift to engine brake it.
8.) Shift up, draft, dab the brakes and arc it into Bentley.
9.) Adjust your direction early for Bacharach. You should be turning before the AI starts. You'll get one or two more passes here.
10.) Your speed will still be decent so on the way to Gambon, you'll get another pass.
11.) Starting the second lap, you should be in 4th place. By Chicago, you can be in 1st place.
Good luck, the last Top Gear challenge is a cakewalk!