HERE IS THE COMPLETE DISSECTION
The Chicago and Calumet Rivers originally flowed into the St. Lawrence by way of Lake Michigan, but having been redirected by constructing canals so that the water now empties into the Mississippi by way of the Illinois River.
(A) Rivers originally flowed into the St. Lawrence by way of Lake Michigan, but having been redirected by constructing.
The use of “having been” is incorrect. We do not expect a “so that” construction after “having been”. “so that” introduces a consequence to an action. “having been” introduces the concept of premise. They do not go well together. Moreover we should expect more informations after “having been”, which makes this answer a fragment.
(B) Rivers had originally flowed into the St. Lawrence by way of Lake Michigan, but they have been redirected by constructing.
The use of “had” is incorrect. If past perfect is used in a sentence make sure that:
1. it is really needed (the two events are related, need a temporal regulation, and the earliest event is preceded by a past perfect verb).
2. The verb expressing the second temporal event is in past tense.
(C) Rivers, which originally flowed into the St. Lawrence by way of Lake Michigan but have been redirected by the construction of.
“comma+which” refers to the item directly preceding “which” -except for cases in which a prepositional phrase is squeezed in, between the modifier's target and the comma preceding the modifier, because it cannot be logically placed elsewhere in the sentence. In this sentence the use of “which” is correct, but this rule is good to recall. What makes this sentence wrong is:
1. The lack of a comma after “Lake Michigan” we already have a subordinator (“which”) we do not want another one in the same sentence.
2. The use of “but” baffles and is incorrect. Because of “But” The entire sentence structure is screwed.
(D) Rivers, originally flowing into the St. Lawrence by way of Lake Michigan, but having been redirected by the construction of
Once agin “having been” fits terribly beside “so that”. “But” bewilders the sentence’s meaning.
(E) Rivers, originally flowing into the St. Lawrence by way of Lake Michigan, have been redirected through the construction of