There have been a couple of videos showing this in use while LEE is touting their new products. Just watching the demo shows the amount of movement I would find unacceptable.
If you want another way to mount several presses in the same location, one at a time, try this.
Mount each press on a square of 3/4"-1" Plywood using bolts inserted from the bottom and with enough counter-bore to make the heads just flush with the bottom surface of the plywood.
Remove all the mounting boards and clamp them together. Drill a hole that will allow a 5/16" bolt to pass through, through all of the boards and in each corner.
Place one of these boards on your bench top and locate it as it will be when the press is in use. Drill a hole the same sized hole in the bench using each corner hole as the guide.
Install a 5/16" Tee-Nut from the bottom of the bench in each hole.
Re mount each press and then just secure them to the bench, using 5/16" hex-head bolts and washers in each corner. Nice and secure, cheaper than the LEE procuct, and when the presses aren't in use they can be stored on a shelf, on their own individual mounting boards. The press will be nice and solid so resizing won't tear it off the bench, primers will seat fully, and the whole sense of secure will be a greater to the operator.