Your understanding is correct except for the part where you said "kind of breaks the rule". I know what you mean by that, though. There is no written rule as to what word order is "correct". There only are the most or more common and the less and least common word orders.
「そして全くその通りで私はあったのだ。」 is indeed NOT written in the most common word order, which would be 「そして私は全くその通りであったのだ。」. As many of you would know, however, Japanese word order can be incredibly flexible on one condition --- that the correct particles are attached at the right places.
Grammatically, である can be treated as one word, which is probably why you feel it weird being spliced, but native speakers know instinctively that it consists of two parts で and ある and that the subject for ある could be squeezed in between --- "in (= で) a certain state + subject + ある(exists)"
By placing the 全くその通り part up front, it was emphasized for an aesthetic purpose. As you said, the author could have used は or も instead of 私は or even said just その通りであった（のだ）. However, by placing a 私は in a sentence in a language in which "I" or "me" is not used often, it was also successfully emphasized in a natural way.