My old GT (on 16s!) seemed to deflect really badly off inconsistencies in the road.
Not just bumps and pot holes but even just the painted lines down the middle of the road would have the steering wheel tugging out of my hands. A full geometry set up completely cured it and cost me around £50 locally.
I drive a 3.2 GT with the 18" wheels now and the only time I've had anything near similar symptoms is when one of the front tyres was on the legal limit.
It's worth bearing in mind that if the wheels on the GT are set up properly, the wheels have a toe-in (that is to say: the wheels sit slightly further out on the bottom edge compared to the top if you look at them down the edge of the car). It improves the handling but the flipside is that on the 3.2, it chews through the inner quarter of the front tires which isn't always immediately obvious when looking at the tires since it's the inside edge.
If you go back to see the car, it's worth getting it out into the car park with the wheel turned all the way to one side (don't turn the wheel whilst the car is stationary). and having a look at the inner quarter of the front tires. I'd put my money on one of them being badly worn on the inside or, atleast one of them being far more worn than the other. For some reason it's always my righthand (drivers side) tire that wears out first but I coudln't say if that's just a characteristic of my car or is the same across them all.