I was listening to the radio yesterday, and they had an interview with Kenny Kramer, the real Kramer, and he was talking about the show.
He didn't sound anything like Kramer, and he actually talked with a New York accent (it's funny how all those shows like Friends, Seinfeld, Caroline in the City, etc. are all taking place in N.Y., yet none of them have the accent.)
He mentioned the Contest, and he said that it actually did happen, except in reality he didn't enter it, because he knew he would lose.
He also said that when Larry David was planning to start making the Seinfeld Show, he approached Kenny and asked him if it was ok to use his character. Kenny said that he asked if he could play the part, but they told him that he wasn't right to play Kramer. When Michael Richards started playing Kramer, Kenny says he didn't even visit with him or speak with him about the part. They only met after about the 35th episode.