Well I would NEVER have bought the Driving Force, you should have gotten the Wingman FF. I've got two of them and never have problems, but people with the Driving Force always have problems and the not-being-able-to-shift-down while steering is really going to hold you back, as well as the 75% braking problem. If you can still trade it, trade it back for the Wingman FF.
However, the centering problem can be fixed easily enough. At the logitech website there is a little tool, then you plug in the wheel into the USB of your PC, and with this tool you can recentre the wheel. After that, at least your centering problems are history.
The MoMo Racing is probably one of the best wheels for GT3 but they've discontinued it in favor of the MoMo Force, which however isn't compatible with GT3. Stores which still had the MoMo Racing have often reverted to its original expensive price, knowing there is still demand for it. However, the MoMo Racing only works with GT3 and with hardly any other games.
The Wingman FF, since it is equal to the GT Force, is the best all purpose wheel for the PS2 as it was the wheel GT3 was designed for and it is sort of a factory standard for any driving game being produced.