I don't believe that Mat is a Hero reborn. Aside from being Ta'veren, Mat's strength comes from the memories that were used to fill the holes in his memory. He asked the people on the other side of the twisted doorway to fill the gaps in his memory and they filled them with the memories of the greatest generals throughout history. Most of them from Manetherin. This ultimately makes Mat the most effective, not to mention lethal, general that's ever lived.