I feel your pain...but I think I'm able to answer this.
First, let's quickly review relative clauses. From Niwasaburoo:
私が買った辞書, which would be the relative clause version of 私が辞書を買った。
私が日本語を教えた学生 ⇒ 私が学生に日本語を教えた。
母が買い物に行ったデパート ⇒ 母が買い物にデパートへ行った。
○毎朝いっしょに学校へ通った友達 ⇒ 毎朝いっしょに友達と学校へ通った。
So there's a lot of construction of the case of the head noun from context. So how are we supposed to reconstruct what the noun's original case would be in ~というN? Well, let's just assume that it's the subject が. In that case, we'd get Nが〜という。If N is こと for example, we'd have ことが〜という。
Now let's take a look at the definition of と from dictionary.goo:
This is huge...because this is NOT what the English word "quotation" means. From this definition, it would appear that と is extracting the substance of what it is quoting more than just the words.
Now if only we could grab a definition of いう that states clearly what it is that the subject is doing with the "quoted" material, and makes sense why this would be metaphorically related to the act of speaking, but it is here where the dictionary flounders a bit. From the という entry:
It would be great if there were a more abstract stand-alone usage of いう to help us understand という, but it seems there isn't.
Two more things I would like to bring up. The first is apposition. In Masahiro Tanimori's Handbook of Japanese Grammar, という is defined as:
- After noun is apposition to the following word.
and 2. After statement in apposition to the following word.
I found this to be helpful to coping with という. Also, the distinction between restrictive and non-restrictive apposition(referenced in both the relative clause and apposition wikipedia pages) is I think good to know.
Lastly you were wondering why someone would use a complex sentence? Well, when you're dealing with 形式名詞(もの、の、ところ、etc), usually you have some manner of cleft sentence. Why use a cleft sentence? i.e. Why say "It was the Germans who started this war" instead of "The Germans started this war"? Well, usually this is wrapped up in the concept of focus. When you say 〜ということは, you're making a note in some global variable called 文脈 that you will be answering the implicit question you have posed. Similarly, "It was the Germans who started this war" is answering the question, posed or not, "Who started the war?" By using a cleft sentence, you set this kind of special focus on some block of dialogue.