Because rabbits groom so much, dyeing may or may not work. Even tattoos can fade sometimes. Every Broken's pattern is like a fingerprint (I once had a Mini Rex that I named Hosanna because she was born on Palm Sunday and the white on her face made the shape of a cross). If you can find something unique about Buttons, it will be nearly impossible to get it wrong. The thing that jumps out at me with Buttons is the nose marking.
A mark that pretty much covers the whisker pads and has a fork that runs up the nose is called a butterfly. Looking at the pictures you have posted, it looks like you have one bun with nose spots, and the others have butterflies. Buttons appears to have a small white mark at the bottom of his/her butterfly, that at least two of the others don't have. Does that help?
..It was like herding Rabbits to get them back inside. 
..
..
...
..Holy smokes. Once caught they are easy to handle..
...
...
