Clause acting as an object complement
Solution 1:
[1] The sky grew dark.
[2] They made him captain.
[3] Books and words have made me what I am.
In [1] "dark" is PC (predicative complement), but it refers to the subject "the sky", so it is subjective, not objective.
In [2] "captain" is objective PC, as you say.
In [3] "what I am" is not a clause but a noun phrase in a 'fused' relative construction, where the meaning is "that which I am" (or, depending on context, "the person that I am").
The NP functions as objective PC, just as "captain" does in [2].