We have traveled through Baltimore and Washington during those hours and also on weekends. There is traffic, but not nearly like a week day or rush hour. You should move along very well at that time in the morning. We once went through Washington at 6 am and traffic was already starting to pick up. My point is, I don't think you need to look for an alternate route that may put more miles on, if going through Washington at 3 or 4 am.
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