(A) According to his own account, Schoenberg, in his String Trio of 1946, was depicting in musical terms a severe physical debility he suffered in the summer of that year, during which his pulse temporarily stopped and he was given an injection to the heart.
Yes it has everything in place let us hang on to it
(B) Schoenberg, according to his own account, in his String Trio of 1946, during which his pulse temporarily stopped and he was given an injection to the heart, was depicting in musical terms a severe physical debility he suffered in the summer of that year.
The sequel of the structure of the sentence isn't right it should be other way around
(C) According to his own account, in his String Trio of 1946, Schoenberg depicted in musical terms a severe physical debility he suffered in the summer of that year, when his pulse temporarily stopped and his heart was given an injection.
His heart was never given any injection it was intented to the heart
(D) In his String Trio of 1946, he was depicting in musical terms a severe physical debility he suffered in the summer of that year, during which Schoenberg's pulse temporarily stopped and he was given an injection to the heart, according to his own account.
Here the last term according to his account is out of place IMO
(E) Schoenberg was depicting, in his String Trio, in musical terms in 1946, a severe physical debility he suffered in the summer of that year, during which his pulse temporarily stopped and he was given an injection to the heart, according to his own account.
The initial sequel of sentence and account isn't in place hence IMO A