I've read that stumps intended for raising mushrooms are best if fairly freshly cut ( a few weeks rather than several years) so you might need to take a slice or two off the top of them if you are using them for that, but what a good idea !
Do you have access to a tractor? If so, you can use a lever system with the tractor to try to pull the
roots out - the way the pioneers used to do it, apparently, only they used oxen and horses. If you are in the Canadian Maritimes you might even be able to find someone with draft animals who would like to give it a go. For that system you need the stumps so as to have something to hook onto.
Clearing land is TOUGH and takes a long time. We used to loosen stumps as much as possible with a tractor and then put some sticks of dynamite underneath the stump to encourage it to let go but I don't think that's an option anymore
If you got the roots pulled and stacked in a hedgerow you don't need to burn them, they soon become havens for all sorts of wildlife and plants and gradually sink into a heap of vegetation. They make a great windbreak and give you a nice little microclimate at least for a few years. Or chip them into mulch. Or turn the windrow into hugelculture!
How big are the stumps? would it make any sense to cut them close to the ground then cut out the heart of what's left and use it as a big planter? If they aren't big
enough, something else I've seen done is the stumps cut close to the ground, the centres mangled a bit with chainsaws and a fire lit in the middle. Neither will do much to get the roots out of your way though.
Also, before you thought about fire in any capacity you want to make sure your land isn't peaty or you might never get it out, once started.
Pigs (some breeds root much more than others) have been used to clear land but I doubt any of them would/could do much for tree roots the size you have.
If you want the roots up and don't want to use big machines to do it, then the best suggestion I have is to learn how the pioneers did it with oxen and get ready for some very very long and tiring workdays with good but very slow results. There really is something to be said for machinery in some capacities, I think:)
Good luck!