The sentence is correct as written. While it is long, each of the clauses clearly relates to one another. "Schoenberg" follows the modifier which refers to him; the clause "in his String Trio of 1946" may be removed without affecting the grammar, and the modifier "during which..." clearly refers to "the summer of that year."

(B) wrongly makes it sound like his pulse temporarily stopped during the String Trio, not the summer. (C) moves "Schoenberg" away from the modifier "According to his own account," which clearly refers to Schoenberg. (D) never identifies the central subject as "Schoenberg;" "Schoenberg's pulse" is not an adequate replacement. (E) changes the meaning, shifting "according to his own account" to refer only to the health details of the final clause, rather than the description of the meaning of the String Trio. (A) is correct.