There is a considerable body of evidence that NASA, under extreme poli

My answer is (A). It took me 02:16. It is a bit difficult to choose between (A) and (D).

(B) At first glance, "transposed" should be "transposing" to be parallel with "doctoring".
Yet "transposed" can be parallel with "faked" to be grammatically acceptable. That said, "transposing a film" is part of the "fake" and thus should not be parallel.

(C) No justification for moving "in 1968" right after the subject.

(D) This version indicates that "transposing a film against a moon backdrop" occurred at the same time of NASA's doctoring TV transmissions. That is highly unlikely. "transposing" must have occurred before the doctored TV transmissions.

(E) "transposing TV transmission" does not make sense.

Few things before I attempt this:
a)Verb-ed form and Verb-ing form can be parallel.
b)If a verb-ing form is used after the , it denotes how or as a result of perspective.

A) faked the first moon landing in 1968 by doctoring TV transmissions, transposing
Here transposing fits the bill for its uses.

B) faked the first moon landing in 1968 by doctoring TV transmissions and transposed
This is a classic case of forced parallelism- faked & transposed - Why forced.? Because it changes the original meaning of the sentence from faked something by doing something and as a result something happened to faked something and done something.

C) in 1968 faked the first moon landing by doctoring TV transmissions, transposing
placement of in 1968 is better in A.

D) faked the first moon landing in 1968, doctoring TV transmissions when transposing
till doctoring TV transmissions it's correct but the use of when for transposing messes up the meaning.

E) faked the first moon landing in 1968 by doctoring and transposing TV transmission
As in B it changes the meaning of the sentence.

Answer IMO is A

A) faked the first moon landing in 1968 by doctoring TV transmissions, transposing CORRECT

B) faked the first moon landing in 1968 by doctoring TV transmissions and transposed faked and transposed cannot be parallel for the sentence to make sense

C) in 1968 faked the first moon landing by doctoring TV transmissions, transposing changes the meaning by changing placement of "in 1968"

D) faked the first moon landing in 1968, doctoring TV transmissions when transposing "doctoring .... when transposing" is incorrect

E) faked the first moon landing in 1968 by doctoring and transposing TV transmission TV transmissions were doctored and not transposed whearas films were transposed