First of all, in a home invasion, I wouldn’t use a carbine anyway. I’d prefer a 12 ga. pump shotgun or a large-caliber wheelgun.
12 gauge coach gun for starters, backed by S$W 9mmm
There are some neighborhoods where you should start with a claymore at the front door backed up by shotguns and a bear trap. Certain areas of Detroit come to mind.
I’m with you on using a 12 gauge! That’s our weapon of choice, too.