I am to propose reverse the direction shown in the update.
Logic behind it is quite simple: that lonely yellow square that represents the parking - it is a obsticle of 3x3 size that I don't want to put on my roads.
So it makes far more sense to have said square on the other side of the road - which brings us to the point: cars park slows while they are not needed, but have to start quick, when they get a task assigned (think fire department).
I'd also ask to remove the yellow square being an obsticle.