Elapd. Concur with your suggestion of the spot light shinning down the stairs.
It will give you a chance to verify your target.
Young gun. Like my position to be forward of my family treasures. The bad guy has more options when coming through a door way. They can move side to side in the hall way outside the bedroom or dive through the door to the floor. If he takes the second option you are in a hand to hand shoot out.
On the stairs he cannot move laterally. His options are retreat, drop to the floor or charge. In any case he is still in a limited target area.
The stair also keeps you mobile. In other words you can retreat to an alternate shooting point should that become necessary.
I also would recommend that as part of your preparations you go to a safe place and shoot from a height which simulates the difference in elevation between your shooting position and the point were you intend to engage the BG.
I once lived in a house which had a landing half way up the stair. The point I intended to engage the perp was when he reached the second step above the landing. Roughly a drop of 6 feet. My shooting position was prone concealed behind the wall at the top of the stair.