I have dug out Oak stumps on my property. There is not enough money in the world to have me do it for someone else...
I did use my sawzall, with a 12 inch blade. (You can by a multi pack of blades for the same cost and damage repair efforts to driving your chainsaw into the dirt)
The advantage of the sawzall is that you can dig below a bit, and cut the tap root.
I did find that dragging hard on the stump sideways, then cutting on the other side make the cuts, especially those 1/2 in the dirt worked well. Each root cut let the stump roll a bit more. At first the movement is very little, but as you cut more, it will lay over more.
I have not seen an easy way to do this on the cheap. Rent big stuff, or work hard. If it was easy, many of us would have less stumps.
In reading some of the other responses, I am reminded of the movie 'Fandango' I think. Is there a train track nearby? Maybe you could wrap a chain around it, and have a large hook on the other end at the railroad track, and wait for a train to go by...
Have fun.