I understand this motivation, but I also recognize that if you want to be able to use a gun as an actually effective self-defense weapon, you need to forget a lot of the normal precautions people use to store guns safely.
You said that you'd feel safer with a shotgun; if your home ever was invaded, in the time from when you first noticed that it was happening until you were actually confronted, would you have time to unlock the gun cabinet, unlock the ammo box, unlock the trigger lock, load the shotgun and ready yourself to fire? Probably not.
This means that if you want to actually use it in a home invasion, you'd have to cut corners. Maybe you'd leave it loaded. Maybe you'd leave it unsecured under your bed. Maybe both. Would you feel safer with a loaded, unlocked shotgun in your house? At that point, statistically speaking, the shotgun would probably represent a bigger threat to your safety than home invaders would.