I do things a bit different. I lay the bird on it's back and make a cut in the skin on the breast to start the skinning process. I do remove the wings after skinning. Once the bird is skinned and wings removed, I cut from the shoulder to the tail bud on both sides of the spine down to the ribs. I then put a finger in the craw notch and grasp the breast with that hand while pulling the neck with the other hand to remove the breast. What you get is the breast in one hand and the rest in the other, never touching the guts. The cuts down the back end up leaving the back meat on the breast. I put the breast in the bowl and proceed to work on the rest. The hip joints roll easily out of socket and can be removed with the back meat left on the thigh. I then remove the heart and separate the leg and thigh.
If I am going to be overnighting with birds in the motel or truck where a leg needs to be left attached, I do things differently. I still skin the bird and remove the wings, but I then use the shears to split the bird down one side of the spine and gut it from the back side. I can leave the bird pretty much intact from there and still finish as above once at home. This way I can facilitate leaving one leg attached and can get 2 roosters in each gallon ziplock bag. I usually nip the tendons on either the front or the back of the joint so the leg folds back into the bag better. Once home you can still cut along the spine on the side you haven't split and pull the spine and ribs out with the back and pelvis still in one piece as before. Sounds harder than it is.
Pet peeve- I hate to pull into a field and see bird parts littering the ditches. I don't like the dogs sorting through the mess and know that non-hunters don't appreciate it either. I always carry ziplock bags and trash bags. In years I trap coons, the feathers, left overs, and guts are saved back for that.