I used a welded diff with the 1200 GT5 car (picture avi). Car handled very well on the race track. Never drove on road. The welded diff required a "throw it in there" type of steering, throttle, brake style. If I tried to drive smoothly into a corner it would understeer quite a lot. If I drove like I was a bit "mad" at it things went much better. Biggest thing that I did chassis-wise was to free up the leaf springs as much as I could and install an adjustable panhard bar to allow for adjustment of the rear roll center as track conditions varied.

I agree that the wwelded diff is probably causing the majority of the problem.