Turn the clamp around and you won't have a problem. This is the same double rail clamp that you have, but I converted it to single rail use by using parts from another clamp.
I used that type of post because it's more correct for a bike built in 1959. It absolutely does not slip and I'm no lightweight.
A Micro-adjusting seatpost and seat sandwich is a more elegant solution for double-rail saddles, but I didn't like paying $15 for the sandwich.