I've never had a problem removing plugs by using an impact gun... Seriously.... Works every time and I've never broken one. Just did it recently on a 170,000 mile F150 and on a 90,000 mile Explorer. Just blip the impact gun a few times, make sure the extension stays as straight as possible and keep backing them out.. Blipping the impact gun until they break loose. If one is very stuck you might have to hit the impact for a little bit... More than just a blip.... kind of like taking a lug nut off.
The Ford procedure of soaking... Working them back and forth, soaking some more, etc... Works too... It just takes a while.
Once those plugs are out definitely try to clean the threads and the tube part deep in the head. I have a wire brush with a long handle that I got at Harbor Freight... Works great.. Just be gentle and clean the brush off often so as little stuff as possible gets into the cylinder.
When you replace the plugs go with some nice, one-piece, and easily gap-able ones like Brisk Racing Silver or Accel Silvers. And don't forget to use some anti-seize... NOT ON THE THREADS. But on the neck part that sticks down in the head... This is where it gets stuck... Not the threads... The threads are your ground contact for spark so you want a good connection there.
And have someone check that tune ASAP. Or go with Brenspeed or JDM Engineering for your tune.