How to beat this mission the "right" way:
The Sentinel has a higher top speed than the Sabre Turbo, but less acceleration, so the most important thing is not to fuck up, especially when you don't have any turns coming for a while and you can make up the distance. Take the turns by braking early (normal, not handbrake) so you don't waste time recovering from powerslides.. if you've played GT3 then you're used to that kind of driving.
Nudging his car *usually* doesn't work the way you want it to, because it seems like any time it bumps you it sends you flying away while he stays steady as a rock, therefore I really can't recommend trying to bump him unless you're in the position to t-bone him while he's turning and hopefully get him stuck in a corner, going down the wrong road, etc. Don't bother trying to driveby him, his car's nigh-invulnerable. You *can* try to make other cars swerve into him, especially if you're ahead and he's looking for a way around you.
Watch out for the two cop cars at the intersection southwest(?) of the Washington Mall.. they don't always appear, but it sucks when they do. You can avoid the trap either by braking (hey, you gotta make a hard right anyway) and/or going off the right side of the road, through the bushes. Near the end, you can cut corners that Hilary won't and save yourself a little time and trouble.. one is right before the bridge, and the other is right after it (cut through the bushes where the police bribe is).
If you fail, and immediately try again, you'll still have cops on your ass. This can be a good thing; when the race starts they often either slam into your rear end (speed boost!) or his (sometimes it screws him up). Also, if you're lucky (and in the lead), an oncoming cop that misses you may nail him.