Get a long throw air hammer (3 to 4" or the 3 or 4 X kind) you might have to borrow one from a mechanic. Hold the axle such that is can not move, the mount point should be very heavy. Make a flat punch that fits the air hammer.
Put the air hammer on the bottom and let it do its work. If you put a spacer on the bottom of the king pin it might not even get damaged.
If you do not have access to an air hammer, than two heavy sledges. Put one on the front side and hit the rear side. The idea is to make lots of shock to break the rust loose. The air hammer was very effective in removing spring perches. We were surprised with how well it work when my brother and I tried it.
Of course, a big press can work too.
The axle should not be heated much above 300*F. That is about the point grease and oil start smoking.
The king pin tool listed in the catalog is probably not strong enough. The one I have does not look like it has good enough threads for a really stuck king pin.