How about Sarah Palin? Win-win on the gender and the cross-over fronts!
Seriously, ugh the thought, but Biden did babble about "healing the divide" and cross-over idiocies until he was suddenly put on the spot in the debate and responded with the easy identity politics "yes" instead of responding with the presence of mind of Bernie to distinguish between a woman candidate and a candidate who is good for women's issues. Other than Sanders, I can't think of a man who would place better than 4th on the list of Biden's VP candidates. I actually can't think of any non-woman I would have been excited by for Sanders' VP pick, but he showed presidentiality in refusing to be played into a locked and constrained position by a silly question.