We have closure! The winning solution was to split the trunk into four different pie slices. I notched the trunk so that I could rest a bottle jack sideways.
I consistently underestimated the forces involved with removing a stump. I'm able to push some of the smaller trees that are 12" or less but the force involved with the bigger ones are exponentially greater. I realized how futile my efforts were when I couldn't even pull out 1/4 slices without breaking chains.