Multiple shotguns that are stashed throughout the house would be my choice of dealing with home invaders who are thorough, determined, violent and willing to spend a day destroying your home for their purposes. Various types of ammo from slugs to 00 buck will handle everything.
One problem with that idea. If the invaders are armed criminals, you are good to go. But if they are LEOs, who look and act just like criminals, you will have committed armed homicide of an LEO, and will either be killed, or sent to prison for life.
So the best initial course of action has to be discretion, with the idea of preserving life and limb, even if you have superior firepower.