I stick the pony head first into boiled water if it's getting a reroot or hold the tail and hair up and angle it so that the neck area is in the water if it isn't. You can gentle pop it off.
With the body, I leave the neck plug attached by a flap and don't cut all the way around. As long as you make sure the plug is level and the neck plastic is glued TIGHTLY against the plug and doesn't bump out, particularly in front, it should be fine.