I guess I don't think of shotguns as being for home defense and when looking at the property and what it's used for, it's for hunting. I think it would be unusual to go hunting with various slugs right? I thought this is what was unusual. Reading your reasoning about the various slugs and what order makes me feel sick because if Alex intended to just wound Paul first and then kill him, that is even more horrific.
I will say if we have an intruder in my house and my husband is home, the intent is not going to be to wound him first and hope he leaves. My LE military husband is trained you don't shoot unless your intent is to kill. It sounds harsh, but wounding someone and hoping they leave or that you can get a second shot off if needed is risky.
The bird shot can and does kill. So yes, our intent would be to kill, but the length of time in between shots would be...one second? It's a semi-automatic.
No, it's not unusual to go hunting with various slugs. It depends on the type of hunting. A person is likely to load buckshot and then a slug for deer, elk, moose, etc. If you're out hunting and you run into a bear, a bear is likely to still charge you if you shoot it with buckshot (there's no need to shoot bears where I live - they are shy, but I'm talking about Alaskan bears or Wyoming/Montana bears). So if you're deer hunting, you're prepared with a couple of rounds of buckshot (or one round) and then a slug (to put the animal out of its misery - or to shoot a bear). I know people who do all slugs, of course. I know people who use a knife for the lethal moment.
But my dad and his brother (both real cowboys, both hunters, and my dad was an army sharpshooter and a lifelong gun enthusiast) always put birdshot in first. And my classes have taught me why. Let's just say that you're less likely to miss your target with birdshot, and whoever gets shot with it (even a bear) is not going to take it lightly. Most creatures will be down (and birds will likely be dead).
Intent to kill WHAT is the question. I do not want to have the intent to kill Bad Guy and accidentally kill the neighbor walking down the street in the middle of the night (or in their car, actually). I think putting only slugs in, in a suburb, is irresponsible unless the crime rate is super high, I guess. Even then. And shooting to kill a person can end up shooting someone you didn't mean to - it's very common. So we prefer to stop the person (and are completely prepared to continue shooting if necessary - all of it with the clear idea that if we pull a trigger, we are trying to kill someone, obviously).