Why on earth does the phrase “As you know, …” exist in dialogues? Why would any person ever use it in conversation? It does occasionally come up in lectures and presentations, but then it means “as you should know, but I am saying anyway to spare you the embarrasment of asking the question, …” When you know the other person in a conversation knows these facts, it just makes no sense. Even as a writer, if you want a character to say something that is redundant because everyone in the conversation knows it, why would you draw attention to it by adding “as you know”. It might have gone by unnoticed that the statement was redundant for the characters if those words hadn’t been there.
Don’t draw attention to your flawed scene setup!