I'm no expert when it comes to GT, can't drift and know nothing about tuning.
I did however just complete the above task but 100th of a second.
I turned all the aids off, had it as standard mode with manual gears.
you really have to use up the 10 minutes also push the gears to the limit (work out when to change gears)
every corner has to be tight as possible, a little break mixed with a change down in gear. now and again you can slip stream for just a second or two before the other car pulls away which will help.
I did not drift and turn just kind of skidded a little into some turns. I think I completed it after about the 5th lap going round