Interesting how this compares to ほど. It looks like they both have “to the extent that” meaning, and the only thing changing seems to be the order of the reason and the result clauses. Very convenient 
苦しさの余り、大きな声を出してしまった。
大きな声を出してしまうほど、苦しかった。
These two seem to mean the same thing to me.
For this section:
Caution
The tense of the overall sentence will be dependent on the main clause. Therefore, it is common to see the verb before あまり being used in several different tenses.
I’m not sure what part of the sentence is the main clause in this grammar point. I think it’s part B? I feel the explanation could use more detail, like specifically which part of the sentence is the main clause, and what do the different tenses for the verb before あまり achieve?