One of our culverts had earthen, natural-looking stream banks on the inside of the wingwalls on the downstream side. In this scenario, should the first bankfull width be taken inside the wingwalls at the beginning of the earthen banks, or should we move downstream beyond the end of the wingwalls?

Because these earthen walls lie inside of the wingwalls and are an extension of the stone wingwalls (just a different material), you should still take the bankfull widths outside of the extent of the wing walls- move further upstream or downstream.