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You could put a couple of nuts on the same side as the stuck cone and tighten them against each other: they'll be secure now and hold the axle still while you work on the cone.
With the axle out of the hub you can try loosening the cone in both directions.
A note of caution: cone spanners aren't intended to take much torque, so be careful you don't end up trashing your cone spanner for the cost of an axle!
Great thread. It's helped me change some bearings in the past but now I have a problem....
I've managed to remove all the cone nuts from one side of the axle, but it seems that the nuts on the other side are quite solidly rusted to the axle. I've tried securing the other side back to the frame with the track nut, but it just ends up unwinding the axle when I try to remove the cone nuts from the seized side.
Before I simply buy a new axle assembly, are there any other tips? I've tried a soaking of plus gas on the relevant side.