Drill holes into the stump with a large diameter drill and then fill the holes with chemical fertilizers. This can soften the stump and then you can use pickaxe to break up the stump from any angle that you think fit and safe. :D
That seems not a big task. Powerful chain saw can do what you want. First remove the upper side of the stump that is getting outside and then slowing move down in the same angle. The same thing you can do with the other part of the stump.
Why not to look for burning the entire stump... it is quite easy, cheap and quick process. However, you need to have few few precautions and guides on how to burn the entire stump efficiently ..... But, I suggest hire a professional tree surgeon or tree removal company to do that work for you...