Sorry but, McLaren F1 Base model and BMW Z4 GT3 (with stage 3 engine tuning - nothing else) have been the two cars I use the most for this. Mainly because I love them... I really don't know what else to suggest if you've struggled with them (other than the GTR R35 TC posted above. Very good car). You could try using HaB-Racing's tune for them - I do.
You can get away with racing softs until you pit as well, if you wish, although it's not the best solution, it may help. They don't wear out at the same rate they should do due to a bug. Pit on lap 6 for fuel and slap some racing hards on and fill your tank up to just under 2/3 capacity and you should come out in 2nd, with 1st not too far ahead (having either caught him on lap 5 or sooner or driven past him in the pits on lap 6). You should finish with just enough fuel.
Other than that, keep trying. It's easy once you know how and the best way to know is through practice.