I'm not a big fan of the nylon stocking. Once the bird slides all the way down, it can still work back and forth and that action does  more harm than good.  The best method I feel is to let the bird cool down naturally in the field. Do not put it into a plastic bag until cooled down.  Get it to a cooler, freezer or your taxidermist as soon as possible.  Definitely do not gut it or put it on any game straps.  When freezing, prior to delivery to your taxidermist, clean any excess blood with a damp rag or paper towel.  Put bird into a plastic bag of suitable size to not bend any of the feathers and seal the bag to prevent any freezer burn/dehydration.  Bread bags or tall kitchen bags work well for pheasants.  Simply let the tail feathers hang out and tape around the outside of the bag in the feet area.  Be careful to keep the tail straight when placing in the freezer. 

Whether in the field or back in camp, the first cut should be around the mid-rib cage area, a few inches behind the front legs.  "Remember more is better".  This will give ample hide, whether doing a wall mount or doing a pedestal mount, which usually requires more hide than a wall mount.  Next cut a ring around both front legs just above the elbow.  You actually can complete the skinning process with just these cuts.  If you need to, go ahead and make a "Straight" cut from the base of the skull, down his neck, to his shoulders.  Remember when hunting out of California, the cape must be removed completely off the skull and the antlers cut off.  There must not be any brain or spinal matter brought back into the state.  Any questions on this please call or you may need to contact a local taxidermist and have it done before returning home.