HEAT!
You definitely need heat. Heat and a lot of force. I've given up on dozens (yes... DOZENS) of axles that never came out of one machine or another. After getting things nice and toasty, heavy doses of B'laster and a B.F.H., if the axle doesn't come out, it's sawzall time, baby.
I don't mind making axles, and the steel guy is only a hop-skip-jump away, and it saves me frustration. This probably isn't the setup for you, but I do advise heavy doses of heat, and the slide hammer is the perfect weapon in the axle-replacement arsenal. I've made adapter tools to fit the old 3-bolt hubs, too.
You're well on your way. Persistence will pay off...
~M