I have never done that, but I have done a patch bud, where you don't girdle the whole receiving branch, but only a square from it. The bark really needs to be in slip mode, and to remove a full girdle of the of the desired patch in good shape might be tough. The cambium contact on that would have to be on the bottom union, on the patch you have the sides and top as well. Not sure why not just lop the top of that off as you would not even want the top anymore. Above any type of graft sometimes it is good to half break above the graft/bud and bending it down leaving some of the bark intact for a period until established so the stock should give energies to the graft. I never have real good results with the patch bud but that was years ago and on pecan trees, and nut trees are hard.