I believe the answer is the third choice: Rockwell said that he had been striving to completely capture everything.
Take a look at the word 'always' this line:
"Right from the beginning, I always strived to capture everything I saw as completely as possible" (Rockwell).
The word always indicate that the strive to capture everything started in the past and still continue until today.
The usage of past tenses in first, second, and the fourth option indicates taht the strive to capture everything is no longer exist today.