I too skin from the mouth, skinned one last night and thought i'd share some input on the subject...
First pull cheeks back and poke your knife inside and run knife thru upper/lower lips, scrap the tissue back onto the carcass(sharp knife is preferred)
Pull the lower jaw and poke knife thru to other side of mouth and cut hid off
I then hang by the lower jaw using a bent nail and cut close to the skull and get around the eyes and cut the ears off
Using your fingers poke and push down inside to take hid off carcass
Push and pull action(both carcass and hide) to take the front legs out
Using a papertowel push the flesh back onto the carcass while pulling the mouth of the hide(like drawing a bow)
Pull all the way down until you see the base of the tail
Pretty much the same process as the front legs, push and pull of the carcass and hide to remove the hind legs
Both hind legs off and off to the next step
Take off the hook and pull hide towards you and cut the vent hole off towards the tail, same time while making cut pull to minimize knife use. Before pulling out the tailbone, cut from one slit you made earlier on the hind legs close to the vent hole, move the the other side and complete the cut to the vent hole and finish the other too.
Slide hide onto stretcher and split the tail
Tack onto stretcher and a small amount of using a knife to carefuly take off some of the flesh and done
Sure hope someone understands the process, any other needed explanations would be great.