I would have to say that A makes the most sense. You are correct in your thinking. If you put b, c, d, and e at the end of asleep then these options don't really make sense. Hopefully this helps.
If you are looking for the best ending then I would go for "A" :)
The best option to replace "whenever she came" in the sentence is A: whenever she came, as it preserves the original meaning of Martin pretending to be asleep each time she entered the room. The other options either change the meaning or are grammatically awkward. Thus, option A is the most suitable choice.
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