Why bother having a 44 magnum, if you buy into the self-defense ammo bull?
Here's an example of a 44 magnum HP, 180 grain, going nearly 1600 fps, yet it barely penetrates 12.6"
http://www.brassfetcher.com/180grHorn44mag.html
Such loads are easy to shoot, compared to 240's, and, the light bullets can be going REALLY fast, and still not penetrate much.
I'd consider 12.6" on the barely acceptable side of penetration, very safe for your situation.
http://www.brassfetcher.com/.44 Magnum.html
Seems it must be possible to find a round that goes near 1800 fps, and, might get you, maybe, 14-16" of gello. With the 180's recoil is mild...
Plus, chances are good the fireball is going to blind the guy.
If you go the heavy bullet route, go with 250 grain, or more bullets, moving at least 950 fps, ala Lee Jurras.
By the way, being able to move a 180 grain bullet 1900 fps is HUGE for home defense, with a super soft bullet. The combination of explosive impact, coupled with likely bullet fragmentation, puts the 44 magnum into near a rifle category for home defense. The major advantage is you can have one hand free, open doors, etc., something you can't do with a rifle. Also, you can carry it in positions you can't with a rifle, yet, you are very near rifle ballistics with such loads.