I doubt 4 days will make much of a difference but, I am always a big proponent of submitting as early as possible. If you are already scoring much higher then I would just take the exam 6/20 so you can get your score 7/10. In reality, I think the impact of taking your exam 4 days earlier won't impact your score and, you won't have the anxiety of submitting "late". If you REALLY don't want to take it early, the 4 day delay in submitting app will likely be negligible