The work you describe would require a proper shipyard though! Definitely an drydock, which were much rarer at the time then ramps to launch new ships from.
That said, you do not increase stability by increasing the length, but mostly by increasing the beam, the so called bulging is an perfect example of this. Length increases are mostly done for increases of speed. (an longer hull for a long flight deck might be a good reason too)
I didn't say the increase in length would be done for improving the stability, where did you get that from? I said the stern shape would be chosen like drawn (square rather than "canoe form") in part for stability augmentation. That's entirely different, I'd dare to say.
PS: And yes, obviously this kind of work would have to be done in a drydock, where else? Maybe in a Dutch one, at least the main work until launching the new hull (with engines, propulsion and steering system).