Don’t question your math at all, I took it even more extreme, suggesting that the top 1% own 50% of the wealth.
The issue I have with your theory is that in enables people to not want to do better for themselves. I’m sure that some of those people in the bottom third are hard workers, but as you point out at the beginning of your post it is my experience that if you’re in the bottom third and you’re not disabled it’s because you aren’t working hard enough.
You simply can’t fix wealth inequality by trying to take it away from the top. Just won’t happen. So change careers, work harder, self improve. That’s the way out of the bottom third.