That "God brought you out of Egypt by night" ought to give us a clue as to what this context is about. It is about coming out, the Exodus from Egypt, not Passover night and the slaying of the firstborn. This is what we have called the Night To Be Much Observed (Exodus 12:40-42). Anyone who understands the context of Exodus 12 and similar places can understand that the instruction in Deuteronomy 16:1-8 does not contemplate Passover per se. It certainly speaking of the Passover season, but it is generally describing the Days of Unleavened Bread and specifically the Night To Be Much Observed.