I never skin feet on a coyote unless the buyer makes it worth it, they are used for trim so feet and heads are of no real value to the fur trade.
I used to skin them in about 5 min but I was skinning an average of 15 a day so I had it down. I have always wanted to use a winch, all it would take is a four wheeler winch. I thought if I made a skinning pole that would extend to the ground then extend up, get the back legs started then hang, run the cable through a pulley at the bottom of the pole and attach with a snare loop to each leg then pull.
I built a similar set up at a game cutting shop I ran, I could run deer through at one every 3 min without breaking a sweet and an elk at one every 8 min. but I was using two one ton chain hoists and it was set up so the animal and the hide moved apart so that the knife work always stayed at one level, no bending over or standing on your tippi toes to skin.