I think if you cut your leather to the shape of the pad. Then mark a line parallel to the edge on the back side and skive from that line to the edge. When you glue the cover on use a smooth wooden handle to push that edge down so it virtually disappears.
Mark II has the concept.
The only decent looking leather faced pads I have seen were either done with very thin leather or had the edges skivied extremely thin. Winchester offered leather facing on pads that had faces square to the pad (like SW Silvers pads before they were ground). If you wanted a pad with rounded edges the leather was pulled down to approximately 1/16 " above the base of the pad but did not tuck under the pad as is commonly seen on British guns
As to glue, a friend of mine was shooting a CSMC 21 with the Winchester style rounded edge leather faced pad (installed by CSMC) @ the Metford WI SxS shoot on a rainy day & leather facing came off on the third station. It looked like the leather facing was installed with a white glue like Elmer's. If I was going to do a leather faced pad I would use Barges or the original non VOC version of Plio Bond contact cement.