Cut the stump off as low as possible, drill holes and add nitrogen rich fertilizer. Horse manure will also help. The decaying stump robs the surrounding soil of nitrogen, so fertilizer helps restore this nitrogen and keeps the rot process moveing along. If they put the ingredients on the stump rot product, it would probably have nitrogen as a primary active ingredient. After many months to a year of this, pile on the briquets and cook her below grade
A barrel with both ends removed and air holes down near the bottom, placed over the stump will keep up a good chimney/draft on the coals and allow you to add more fuel and concentrate the heat of the fire/coals onto the stump. Some say soak in some kero or diesel fuel before you burn, but I don't think this helps much as the fuel will just vaporise and burn above the stump, transfering little of that heat energy into the stump.
Safe way to pull with cable and winch? leave the stump a bit taller for leverage. Dig and cut roots, as many as possible, particularly on the side opposite the pull. Soft ground helps also, if you can reach the dug area with a hose, all the better to soften things up. On the cable used for pulling, place something soft/bulky about mid span on the cable(heavy coat or horse blanket). Wire rope dosn't typically store too much energy. If you part a cable or loose your grip on the stump, this will help absorb the energy and direct the cable toward the ground.
Trees are strong in the horizontal axis as they resist wind all their lives. They are not typically as strong in the vertical axis. If you can get an old truck rim to run your cable up and over beside the stump, this will put a vertical component to your pull and help lift the stump up out of the ground.
Good Luck