Count your right but still at 10 yards your saying birdshot isnt enough to penetrate and kill and intruder? 10 yards in a home is max distance in reality we maybe talking 5 yards realistically. So at 5 yards birdshot wont kill?
People have survived shots to the upper torso and even the head from 12ga loaded with light birdshot at distances closer than 5yds. Birdshot may penetrate deeply enough to force a physiological stop depending on the scenario; but it is less likely to do so than heavier shot.
As I mentioned earlier, at 10 feet the deepest penetrating #8 shot is around 5", with most stopped by 3" - and that is in bare jello. Are attackers typically naked invertebrates where you live? Will 3-5" make it to their vitals from every conceivable angle? If so, #8 shot may work just fine for you. If on the other hand, they might be homo sapiens, I'm sure some measuring tape can show you how little penetration is left in #8 shot if something like an arm gets in the way.