I just watched your replay, and it really isn't that bad. You're not jerky, you're not locking up, and you're in control of your car very well.
Too well, actually.
You need to drive more like a maniac to be on par with the leaders.
Quite simply, you need more speed. Your apex speeds were 20-25% off the WR speeds (try watching a few replays; compare the speedometers). Losing that much momentum hurts your straight-line speeds in such a slow car, and that's where most of the time is lost.
So how do you get better corner velocity? You need oversteer. Brake later, and continue later into the corner. With a rearward-enough brake bias, your rear end should start to go out a bit. Sliding loses a lot of speed, however, so you have to be very smooth. But losing some speed is a good thing, as long as you enter the corner with a big enough head of steam. The idea is to scrub off just enough speed by the point you hit the apex that you can go full throttle again the whole way out (if you can go full throttle before the apex, you weren't fast enough on the entry). And be sure to use the whole curbing on the exit; there's no reason to jump back into the middle of the road so quickly. (Try to turn as slowly as possible on the straights; any lateral movement scrubs off speed.)
Just a few other notes. You had a full tank of gas, which is not what the leaders use.
I don't know how much time that costs, though, but it is probably over a second (maybe two) for that car/track. Also, if you really want to challenge the leaders, having your tires at 50 degrees all around is worth a few tenths, at least (good luck getting the rears up there, though). Finally, I really don't know much about setups for that track. I have had the most success using a very stiff rear and a soft front, in order to maximize oversteer. But I'm still a second off the WR (although I am only using a mouse), so what do I know?
Good luck. You will get better.