I in the past had a very similar project but it was deer hide, I had the permission of the customer to hand sew it to the mat, now this could cause some damage each time you put the needle throw the hide. I first drymounted the mat to the backing (artcare foamboard)then that gave my mat enough strength to beable to support the hide but also made the mat strong enough to stretch the hide as you are sewing it, having the hide stretched will pervent the middle of the hide from saging. The hide that I framed was fairly large about 40"x40" good luck and make sure you get the permission of the customer before you do sew it just incase it isn't okay with them.
We are currently doing a deer hide with the complete Battle of the Little Bighorn beaded as a design on the hide. Presented quite the problem since finished size will be 57 x 70. With the owners permission we are mounting suede fabric to 3/16 gator board for rigidness and sewing the hide to the board. We are then using slats on the side of the frame to lift the plexi. We are taking before and after pictures and will send them off to Decor and PFM and hopefuly they will get published! If not at least I can publish them on a web site in the future.