The only time I pulled a stump, I used a sawzall and a lot of blades. Took a lot more time than I expected. Lot of root. Chainsaws are useless, the chains go dull instantly. I used a come along to the bumper of the van, and pulled out the rest of what was left.
A combination of things might help. Winch to tilt the stump, and expose roots.
If fire is an option, drill plenty of holes, and use a shop vac to draw or blow the sawdust out. Let the stump dry for a couple days, and burn it out with kerosene. After the stump starts burning, use the shop vac as a blower, to make a blast furnace, and burn it out faster.
I've heard of drilling the stump, and then pack with powdered milk. Speeds the decay.
In any case, please write again after the stump is out. Let us know what worked for you.