Ive was taught how to skin one by hanging them head down. Never tried it any other way. Hang them up and slit the throat to try and drain some blood and work away.

I didnt notice anybody say they debone as they go.
I find it easier to go ahead and debone the meat starting at hinds and working down getting the meat off the bones and throwing it in a cooler of cold water.
When we are done just wrap the cap back along the deer and load it up to haul it to the bone yard. Havent used a gut bucket in a long time.