Pine trees can have a DEEP tap root, if you can dig a deep trench on one side to expose most of the tap root you may be able to push/pull it over, then pull it out?
Had almost the same suggestion... go deeper and wider so you can get to the underside better. With the BH sitting at the edge of your hole, you don't have the reach to get underneath the stump any further, but you're not out of options by any stretch. Make a ramp down into the crater, then drive the backhoe down the ramp so you can dig more underneath the stump. Eventually you'll remove enough material that the stump becomes unstable and you can topple it. That is one big honkin' stump, so be careful where it falls!
Then you can grub more soil away until you can move the actual stump, probably pushing and pulling with your equipment.
Please be carefil when working under the stump. We had a professional logger "disappear" from a worksite. They did not find the body for years. He sat in the shade of an upturned stump to eat lunch; it reverted backed into its hole with no trace of the event.
Well between the L35 and the cat skid steer, we got it out. Neither one of them could pick it up so we used both backhoes to clean enough dirt off to lift. The Cat rocked all the way back to the side of my hill where I dropped it.
Then since the L35 was here, we've replaced the 36" diameter pipe that serves as the bridge to my house.