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.