Why machinery order changes capital-ship survivability

Would moving the engine rooms ahead of the boilers make the propeller shafts longer and more vulnerable?

Yes, but the layout can improve magazine temperature control, subdivision, and separation between boilers and magazines, creating a different survivability tradeoff.

Moving the engines forward lengthens the propeller shafts, but it also separates boilers from forward magazines and spreads vulnerable spaces through the hull. Dense engine machinery can intercept fragments differently from a boiler, which behaves more like a pressurized hazard when struck. Keeping boilers and magazines apart also helps with magazine temperature control before battle damage occurs. The arrangement therefore trades some shaft complexity for subdivision and a reduced risk of one hit linking several catastrophic failures.