Looked in a mirror and realized my eye sockets themselves are not perfectly horizontally aligned. One is slightly higher than the other. Don't know if that's the cause. Maybe I'm like Dr. Frankenstein's Monster. Could also be an inner ear defect, I suppose. But my eyesight is fine.
So I fitted my Nikons with the same gridded 'E' type screen mentioned above. It's used for architectural work. That did the trick. But now when the grid says it's correct, it still feels wrong to me. And when it feels right, the grid says it's wrong.