I'm getting the willies just thinking about this -- talk about getting waaaay out on the limb!
If you do take a stab at this, do it in shallow water and by all means have someone filming it... Strike that last bit -- your insurance company may subpeona the film to negate your claim
Seriously though, why take the chance? It sounds like you're planning on being shaftless for a fair amount of time, and the gremlins are going to be working overtime trying to figure out how to defeat your best laid plans.
You could just bang a wooden plug into the hole (consider it a dress rehearsal for a mid-ocean damage control evolution), and then drive it back out with the newly finished shaft. That'd be a little faster than fussing around trying to get a threaded cap onto that gushing geyser.
Anything you could do to raise the stern (and thus lessen the ambient water pressure) would probably be a good idea as well. The closer you can get it to the surface, the lesser the pressure will be.
Do think long and hard before you actually pull the shaft out. Consider everything that could potentially go wrong and take countermeasures to mitigate the risk.
Hope it all comes out (and goes back in) well.