I agree that your version is better. To me, a slip of the tongue is when you say something you didn't mean to say but it's still a real word that usually fits the context. Some can get you into trouble. I used to call my children by the dog's name because I'd had the dog a lot longer. That was a slip of the tongue.
When you say tongue twisters, you often don't say real words, or they are real words but not at all in the right context. Getting your tongue all tangled up is a much better way to say that!