My choice would be 7.62 x 39 here... almost the same, for the same reason.
I agree with your take on it.
.223 is for plinking IMO. If I had someone giving my family trouble, I would want my rounds to scare the crap out of them to discourage them and drive them off.
Something of that caliber slamming into wood around the assailant, would cause them to think twice.
7.62x39 is a great all-purpose round, and it’s suitably between the heavier .308 (7.62x51) and the smaller .223 (5.56). If you want to varmint hunt, plink, or wound, .223 works. If you want to hunt big game or men, .308 is the way to go.