I opted for a pre-7am start and the most wind-sheltered route in, so wasn't unduly troubled by crosswinds blowing me into any vehicle's path, for the simple reason that there weren't any vehicles on the north/south roads at the time I used them.
The bulk of my ride was directly into the wind, so I did indeed take the Croix and spent essentially the whole time tucked down in the drops, with my face telling me I was going 40mph and the GPS saying 10.