I don't think mixed would work, the men will be quicker.
I don't see why they cannot run them at the same time. Roads are already closed, cameras in place etc. If they need to, run each stage a little shorter, have the women start from a different point along the route and set them off before the men. That way the men won't catch up to the back of the womens race and the spectators have two top class races coming through for the price of one
I think the spectators, sponsors and TV would love it, surely there must be a way of making it work.