What are people actually using for the driving missions?

Stock pad has been completely fine for me until the longer chase sequences, where I start losing precision about eight minutes in. Not sure if that is the hardware or just me.

What are the people posting clean laps in the Garage actually holding?

Eight minutes in is a grip fatigue problem, not a precision problem. Before you spend anything, try dropping your steering sensitivity a notch — most people run it far too high and compensate with constant micro-corrections, which is what actually tires your hands out.