The Veyron is over 930 lb-ft of Torque so its not as if its impossible
Then you'll say put bigger wheels on it, but the G65 has problems turning as it is. It's top-heavy and live axles front and rear don't help at all.
I expect its high ride height and archaeic suspension don't help either.
You could keep tweaking every single part of the car, but if you were to get it to a point where it can handle as much power as you can possibly screw out of the Biturbo V12, it wouldn't be a G-wagon anymore.