I just watched your replay, maybe I can help (I do 1:08 quite easily :P).
First, your rear tyres are not warm enough. Wheelspin at the start will help.
Then, you turn in very early at about every corner. Turn in just a bit later.
And you need to go through the corners a lot faster. I see you got problems on the exits. Don't let your wheel hang in 1 position through the whole corner. At the exit, try to aim a bit more to the outside of the track, use more kerbs.
And if that still doen't work, try to drive through the corners where you got problems in a higher gear, so when you change gears you don't spin that fast. And if even that doesn't help, add more rear wing.
Good luck.