I dont have a backhoe, nor stump grinder.
2 years ago i cleared a couple of oaks that had their roots sticking out of the ground, they dulled my mower blades and broke tines on the rake so at least the roots had to go.
I chopped off two 5" roots with an axe, then hooked the chain on them and pulled them out very easy, over a length of about 3 yards before they got so thin that the ends snapped.
Because i removed 2 fairly big roots i was afraid that someday it might fall on my new fence along the wood during a storm. To test the tree, I backed the tractor up into the fencerow and hit it slowly with the grill guard. it started waving its crown way more than i expected, so i decided that the whole tree had to go.
I intermittently pushed to get the tree to wave stronger, and then pushed on from the dead point of the wave onwards, and pushed the tree over while most of the roots broke during the fall.
Then we chopped the trunk about 4 meter above the root ball, dragged the crown away to a spot where my neighbor sawed it to pieces, while i kept working on the root ball.
That was a 15" oak, and it was turned into firewood, gone with roots and all within 3 hours.
If you chop off the roots and pull them out one by one, you will have the least work with it afterwards, backfilling the spot when the roots decompose.