I know there are people who have made it though this, but S7 is absolutely maddening. I've been playing since GT3 and have never had the trouble on a mission test like this. I've made gold on most of the other races but there is something about this one that just isn't right.
I've tried a lot of cars and settings, but come closest with the Amuse and the GT lm. I say closest because I can turn laps at 1:39 - 1:42. And I've done this so many times I think if you don't hit under 1:42 on the second lap, you have little chance.
And if you manage to hit that time, one of two things happen. First, there can be two or three cars so far ahead I know going into the 4th lap it's mathematically impossible to catch them. And if that happens, I just exit the race right there. Hitting that time is a problem if there aren't any cars in position to draft on the straight.
The other thing that has happened is that races where I do get close, up to 5th or 4th place by the 4th lap, I'll either make a mistake, another car hits me (I get the collision penalty), or a car pushes me off (I get the shortcut penalty), then a train of cars pass and finishing 3rd becomes impossible. I've even been rammed into a car and taken a penalty for that (usually a 7 sec penalty).