Only after weeks of calling ______________________________ to get my money back.

The phrase "Only after weeks of calling" sets up a sentence that implies a certain structure which is typical in formal or literary English. The correct completion of the sentence needs to maintain the emphasis created by "Only after," which suggests an inversion in the construction following it.

The phrase "did I manage" fits perfectly here because it is structured to create an inverted sentence, which is common in English when beginning with a word or phrase that indicates time, such as "only after." This inversion emphasizes the effort involved before achieving the outcome.

Using "did I manage" suggests that after all the effort and frustration of weeks of calling, there was a successful outcome, which is exactly what the sentence is conveying. The other options, while they all maintain a sense of achievement or outcome, do not align with the inversion required by "Only after," and therefore, do not complete the sentence correctly in this context.