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So let me make sure I've got this right? Your car is just about maxed out in mods aside from a few things and you'got perhaps medium soft if not soft tires? With ASM on midfield?
I can't upload any of my drift replays because I have neither a sharkport, nor a video capture card

... there are some videos around by others that show cars like the Grand Sport and then some are driftable.
Here are a few suggestions I'd like to give though.
First off, make sure ASM and TCS are both off. Second, I'd suggest if you have money in your account on GT3 to get another bone stock Grand Sport, and get that on simulation tires. Try a track out like midfield, or Trial mountain or some course, why?
A thing at the least I do to try and get a car to drift is not to mod it hell off the line, but first try and see if I can drift it stock on simulation tires and see how it behaves. Once I can get it to drift and understand it, then I start either peice by peice or all at once given mods. Excluding my Camaro, I've left the weight stock and left no changes I could not undo including port polishing and weight reduction to name two.
I would not try and get the car to be too big on power to begin with, I'd try and work with the stock power of a given car best you can less it's that difficult to drift with, less you either try and learn how to get a said car sideways well and also if you do have stuff like a full racing suspesnion, to tinker around with the car to see how you can get it so it can react more to what you want it to do.
But working with a car bone stock before moding it, though a long process is a better one. Having a fully moded car in even one direction could be in one sense good, but if one only can drift with a fully moded car, I think something has to be said about that said driver. In short, before you go for the full mods, just go and see how the car works bone stock on a said track (Midfield is good I guess, but I lean more for Trial mountain, also Laguna Seca, Grand Valley, and Seattle, also Tokyo RT 246 and Speical Stage Route 5, also 11) on sims with no TCS or ASM, why?
TCS and ASM try to have your car regain traction by reducing throttle input and other things, they can be a hinderance, also, the high grip tires, though would be good for the higher bhp cars, espically with lower weight, at times can run a double edge, though guys like DR and Swift know more on that subject better than me, you could ask them thru a PM or use the search button for a thread on tires and such.
That's about it, dunno what else to say, on end I would be surpsied no one else is replying to this (least when I wrote this down), then again, GT4 is out so GT4 is as will Smith (agent J) from MiB said... 'the new hotness'... (dang that was lame...)...
Till later.