if you're facing it, why would the leather need to be super thin? couldn't you use a little thicker leather (3-4oz maybe), glue it on, trim and sand the edge to a perfect fit, then burnish the edge to finish it? The picture you linked to looked like the leather was substantially thicker than what most people use for covering.
I'd be willing to bet that's part of the reason they were faced on the first place. heck of a lot easier to glue leather to one face than it is to wrap it around curves, and covers the screw holes without plugs too since it's applied after the pad is in place.
if you want the edge of the leather to roll down onto the pad so that there is no exposed edge, I think you'll want to use a skiving knife the taper (or skive I guess) the edge and allow the rough side to tuck under. That's how they do high end leather seems and edges that would be too thick otherwise
