MTMilitiaman, please excuse my ignorance for my leading men through three Infantry deployments and service as a trained Sniper does not measure up to your vast real world knowledge and experience.
I am extremely proficient with an AR platform. For close quarter defensive battle, the shotgun is superior. Yes, you still have to aim. 00 buckshot is more likely to stop the intruder in their tracks than 5.56, even if I miss center mass. 5.56 to the shoulder or leg may not prevent an intruder from moving forward (especially if scared into "survival" mode from the injury). 00 is more likely to put the intruder on his ass. Even if I miss completely, the receiving end of the blast will do more to disorient the intruder. I will have PLENTY of time for a follow up shot.
I can tell you first hand that a 00 buckshot will not do any more damage to your ears in closed quarters than a carbine AR. Different sound, both extremely uncomfortable. BOOM vs. CRACK. When defending my family and self, I can deal with the discomfort.
A very bright TACTICAL mounted flashlight provides the defender with a significant advantage. It is amazing just how effectively the bright light will disorientate an attacker. No, do not walk around with the light on.... making yourself a target. Aim as you illuminate. Fire.
Pistol grips that replace the buttstock suck. A collapsible AR type buttstock on a shotgun is nice. Length is NOT an issue, unless you are using your G-fathers goose barreled shotgun.
Regarding sidearms... I'm not as proficient with a handgun as I am with either an AR or a 870, therefor it would not be my first choice, but a SIG P229 .40 should serve as adequate back-up.
Aside from all the tough guy BS talk about shooting people, I just assume scare the invader(s) off without any blood shed. I have no desire to expose my family to it.