The best alternative if you are unable to use a grass grid system or permeable pavers is to look at actual permeable concrete products. These are porous products made up of larger-sized stone aggregate, creating "nooks and crannies" which allow water to pass through.
The only caveat that I will throw out there is that you may want to check into these products' ability to withstand the abuse of a snow plow. Given their rough texture and uneven surface compared to pavement or standard concrete, I can see how a plow could rip chunks out of your driveway.
For more information:
Read Christian Kienapfel's Ask A Pro Q&A, "We have a 400-foot driveway. Can you suggest a permeable or semi-permeable topping?"