Over five thousand years ago, archaeologists have discovered that Mesopotamian cooks were preparing chicken with coriander and tamarind, just as Egyptian cooks are still doing today.
(A) Over five thousand years ago, archaeologists have discovered that
(B) Over five thousand years ago, archaeologists had discovered that
(C) Archaeologists have discovered that, over five thousand years ago,
(D) Over five thousand years ago, as archaeologists have discovered it,
(E) Archaeologists have discovered, over five thousand years ago, that

Is it a general rule to have THAT immediately after reporting verb without any non-essential modifiers in between - as in E?