Going through each sentence:
A. for
constitutionally discharging any service member for aberrated orientation or conduct, the military
required to first prove that the service member’s discharge significantly
furthered, and was
problems:1. verb to be is missing from the passive verb
2. from the meaning, the military should prove first before discharging. To serve this meaning, the verb 'furthered' should be replaced with 'would further' or any other trick that elaborate this meaning.
note: I think using an adverb to modify 'discharging' which is a noun is not wrong because it is actually a gerund which hold some of the properties of the verb.
B. to constitutionally discharge any service member for aberrated orientation or conduct, the military
was required to first prove that the service member’s discharge
would significantly further, and was
C.
in order to constitutionally discharge any service member for aberrated orientation or conduct, the military
was required to first prove that the service member’s discharge
will significantly further, and
will be
problems:1. 'in order to' is wordy, and can be replaced with 'to'
2. 'was required' is not in tense agreement with 'will '
D.
in order to discharge any service member constitutionally for aberrated orientation or conduct, the military
will require to first prove that the service member’s discharge will significantly further, and will be
problems:1. 'in order to' is wordy, and can be replaced with 'to'
2. 'will require' is an active voice which alter the meaning as if the military is the one requiring others
E. for constitutional discharge of any service member for aberrated orientation or conduct, the military
would have required that it prove that the service member’s discharge would significantly further, and was
1. 'would have required' is an active voice which alter the meaning as if the military is the one requiring others. Also, "would+have+verb" is used to emphasize regret that an action is not done. All these meanings are far from what the main topic is saying.
so B