My 97 SL320 Sport has the same size tires but on 8 / 9 factory AMG wheels.

Wide tires do pickup variations in the road so they is part of the deal. If your wheels have more positive offset than normal you will feel more in the steering. My offsets are 31 front 35 rear.

The first step is to see if the ball joints are seizing up, this will make the car darty as the steering won't self center. Seizing ball joints wont always be loose when checking with a bar.

On your toe settings are they toed out or in? Does anyone have a conversion from degrees to inches? ( the conversion is tire outside diameter dependent )

Within limits, front toe in gives straight-line stability, front out crisper turn in. My car was a bit numb on turn in until readjusting just under 1/8" toe out.

The rear must be toed in otherwise the tail will step out under power. The higher the power the more toe in needed.