3M makes anti-slip, no-skid treads and tape that are adhesive backed. The tread is what I put on my lam sled. The original piece is still on there and works perfect. To ensure the lams don't move at all, I simply hold them down against the sled/no slip surface with my hand... not hard, just firmly, both as I'm feeding the sled in, and catching it as it comes out the other side.
It might work as well if you put GOOD cloth backed 50-60 grit red oxide sandpaper on there with 3M transfer tape or an equivalent product... but the no-skid stuff is readily available too.