Beaux,
I have a backhoe that I use to pull stumps and it works great. It will pull smaller ones in one "scoop", larger ones need to be dug around and worked a little. Of course it leaves a decent hole that has to be filled and leveled. (Since I'm clearing for building sites and driveways, I'm always moving earth, so regrading isn't a big deal.) If you don't want to have to regrade a good portion of the pasture, a stump grinder may be a better option, since it leaves the material pretty much in place. BUT... you'll probably need to remove some of the chips and top-dress with topsoil before you reseed. Or at least mix in topsoil. As for waiting for the stumps to rot, I've got some in my backyard that are rock solid after 5 years. There are forums with lots of suggestions on home-brews to speed up the process, but none of them work overnite.
With a backhoe, you also end up with a bunch of stumps with dirt and roots attached that need to be dealt with. You could end up with quite a pile of those. If you've got an area that you can bury them, you could use the dirt from the hole to fill in the area you pulled the stumps from. Depending on how many stumps you've got, using a backhoe could turn in a several day project.
A stump grinder would probably be the cleanest and fastest if you're renting the equipment. Then you can use your FEL to play with the chips and topsoil afterwards when the rental clock isn't ticking.