Ah, now I see, you are sticking your thumb out. Don't do that. Oh, that is what you are complaining about.
I guess it depends on how far your thumb sticks out. And I don't have a photo of what I am talking about. But when I do what I mentioned to you, the thumb is protected no only by the part of the fingers closest to the knuckle, but the knuckles themselves. The knuckles are protected by the straight line back to the wrist, and up the radius. Is it possible your thumb isn't so much hitting the bag as the sudden stop is jarring the joint and causing the pain?
As to JowGaWolf's video, I would be worried that it would not protect the thumb, especially one that is already incapable of full movement and then might be required to compress more. Even the pointing of the index finger seems more dangerous to me that the way I was taught to use what we called the Dragon's Head Punch. We used the middle finger which didn't so much involve the thumb as it was curled under in a different way.
But JowGaWolf, I realize that often it has more to do with how one learns to make something work than endless bickering on a forum about what is best. If a technique works for the one using it, that is all that is necessary.