Eliminate the appositive/non-essential clause in the beginning to see if the sentence reads well around the commas:

A) Although he is as gifted as, if not more gifted than, many of his colleagues, he is extremely modest and his poetry is unpublished. -- INCORRECT, not as good as C because it ends in the passive voice.
B) Although he is as gifted , if not more gifted, than many of his colleagues -- INCORRECT, doesn't make sense.
C) Although he is as gifted as, if not more gifted than, many of his colleagues, he is extremely modest and will not publish his poetry. - CORRECT
D) Despite his being gifted, if not more gifted than his colleagues, he is extremely modest and will not publish his poetry... -- INCORRECT very wordy and in the passive voice in the beginning
E) Being a gifted as, or more gifted than, many of his colleagues, he is extremely modest and his poetry is unpublished. -- INCORRECT - Starts and ends the sentence in the passive voice