Yes, I realize that. But going back and looking at the blowup of the photo of the left end of the spindle from the beginning of this thread, it would be impossible to literally do what the factory instructions say and achieve anything. However, looking at the blowup also reveals that the large hex nut has to be turned several threads CCW (hopefully at least the threads are RH) before you can drive the spindle much through the gear. And the large nut has to be completely removed from the spindle before the spindle can be removed from the headstock.
It is not possible from the photo to tell how much of a gap there is between the nut and the gear. But it might be possible to move the gear enough to allow the insertion of a pair of wedges similar to the Jacobs arbor removal ones but you will probably have to make them as I don't know of any made that are large enough.
So as I wrote earlier, assuming that you are not going to make the large wedges, add that before beating on the left end of the spindle with the hammer hitting a hardwood block, you must unscrew the large hex nut until it at least contacts the face of the gear, and as you drift the spindle through the gear, continue to unscrew the hex nut. And don't forget before you start, to loosen any set screws elsewhere in components so locked to the spindle (if there looks like there is one in the cone pulley, there isn't - that will be an oil hole plug). And take care of the Woodruff key that keeps the bull gear from turning on the spindle.
Actually, were I doing it, I would use a piece of All-Thread to make a custom puller, as swinging a hammer is too tiresome at my age. I would also cheat and use the hollow piston cylinder from the hydraulic Green Lee knock-out punch set that I have had since before most of you were born. But the All-Thread and nuts alone will work OK.