I have removed several large maple and oak stumps this year and tried several different methods. The best, quickest and cost effective way to get them out is a good size backhoe. Just luck but there is a rental yard a mile from my house. For two hundred dollars I get to play for a day. Twenty-one stumps is the best I have done in a day. These all were between 24 inches and 30 inches in diameter. I also dug a few holes to bury the stumps. Once you get the hang of it, you can dig them out really fast.
I had a couple dozen stumps to remove. Cheapest, cleanest, easiest thing to do is rent a stump grinder--- For $100-$150 a day you can grind dozens of stumps up to 16" below the ground level side roots and all. There are various size stump grinders. Get one appropriately sized for your project.
I can't yet confirm if it works, but my NC mountain neighbors swear that drilling a few holes in the stump and filling them with sugar will result in the stump being gone within a year or two....course then you might have to get rid of the ants and termites....