There's one other method that I have heard of, but not tried is to make up a fixture that you can mount as long a piece of pipe you can ie: 8-10 feet if possible, engage the back gears to lock up the headstock
Please, no. absolutely not. The result will be a broken tooth on the back gear.
what I call the 1000 taps. Like death by 1000 cuts. No big hammer blows, just tons of little ones,
Oh yes.
This is what worked for me with a SB 9c with a rusted on chuck. Lubrication and lots of penetrating oil ... Remove the chuck from the backing plate - it is only in the way. Bolt a piece of flat bar on the backing plate with about 1" extra to tap with.
USE THE SMALLEST HAMMER YOU OWN - but not more than 3 or 4 ounces in any event.
Disconnect all belts and gears so the spindle is free turning.
every time you pass the lathe give it 25 or 30 taps. -- sharp ones firm ones, but not big ones. After 1000 taps or so, feel free to give a few (5 or so) taps in the tightening direction, then 1000 taps unscrew, 5 taps retighten. You keep doing this until the things gives way, which it will, eventually.
The alternative is to cover everything in plastic - I mean EVERYTHING, and slit the backing plate a zip disk. Notice I did NOT say "cut it off". it is very easy to damage the threads: Once you have a little material holding the backing plate on, use a wedge to slowly (and gently) open the cut. Then resume the light tapping: either it will loosen, or the backing plate will crack open.
In my case with the 9c, the rust was pulverized by the light taps and it came off. My friend Bert removed a backing plate by splitting the iron backing plate, so I know it works too.