This is one of the most classic discussions I've seen in a long time. So many widely varied ideas - sacrificial chainsaws, army trucks, pressure washers, bigger machine, explosives, fires - great stuff! Am I the only one who was thinking airlifting it out with a helicopter?!
Seriously though, I've dug out some massive stumps with a comparatively tiny machine. I cleared and stumped a 100 x 40 garden that was oak and pine up to 18 inch diameter - decent size stuff. I did it all with a Kubota
B2630. All it takes is time and persistance. Small machines make you work smarter, not harder. Here are my tricks - many have already been mentioned.
1. Get as much dirt out of it as possible - however you can. Power washer, crow bar, shovel - whatever.
2. Pop as many roots as you can all around the stump. If you can't pop them, work out farther away from the stump where the roots are a little smaller. Also, there are usually roots deeper than you think.
3. This is the biggest trick. Don't use brute force to try and pop it out. It will come out a whole lot easier if you try to twist it, or rotate it in place. 90% of my stumps came out like this. They twist to a point then just pop and you can roll them out of the hole.
Good luck, whatever you choose. I still like the helicopter idea though. Or maybe you could donate it to the air national guard and they could have some practice strikes on it!!