Miele Man

I think that unless you can anchor the frame so that you have two hands free to work on the headset, you're looking at a two person job. I'd get a buddy to hold the bike and I'd try using a pipe wrench to turn that headset part. However, I'd grease all the threads above that headset part to reduce friction as much as possible. Also, as someone else suggested, if you can thread that headset part onto the fork even a bit more that might help you get lubricant (grease) onto all the threads that the headset part will be bearing against as you loosen it.

If there is a picnic table near you I' strap the bike on its side to the top of the table. Then you can apply LOTS of torque to that headset part without much worry about damaging the fork or twisting the frame. I've done that with stubborn headset parts in the past as well as doing that to loosen really stubborn aluminium seatposts in a steel frame.

Good luck and please let us know how you get that part off.

Cheers