井戸掘りからゴミの処理に及ぶ would sound natural, and already emphasizes how broad his responsibilities are.
Slightly literal translation:
井戸掘りからゴミの処理に及ぶ
his responsibilities reaches from digging wells to getting rid of garbage
Adding まで strengthens this emphasis
井戸掘りからゴミの処理にまで及ぶ
his responsibilities reaches from digging wells, to even getting rid of garbage
井戸掘りからゴミの処理まで及ぶ is not grammatical.