The correct completion of the sentence is "She can't sing as well as I had thought," because this construction is used to compare the singing ability of "she" to the speaker's previous expectation. In this context, "as well" is the appropriate choice because it is used to compare the level of ability. "So well" and "good" are not suitable for this comparison, and "well" alone does not convey the comparison being made in the sentence. Therefore, "as well" is the best choice to complete the sentence correctly.