I know the uses of diye in principal: though it looks like a pure mark of indirect speech it is very much used for expressing more abstract meanings, purpose for instance. My question is how much is it really needed for reported speech? Can you do without it? Maybe I´m wrong but only two cases come to my mind where I can´t think of replacing diye with anything else:

* When the speaker wants to report something to the letter. It´s like the reported part of the sentence was irreversibly fixed and the speaker needs to find a way to end the sentence properly without changing anything of what was already said.

         Yarın gel diye bir telgraf çekti.

"Yarın gel" şeklinde bir telgraf çekti.

* In written language when the citation is written word by word and when a verb other than demek denoting utterance is used:

         Kaplumbağa  -  Deli misin?  -  diye bağırmış.

"Kaplumbağa - Deli misin?" şeklinde bağırmış.

I wonder if diye is used at all in other types of reported speech where infinite verb forms are used and where changes in tenses, pronouns etc. take place. Is it?

I believe it´s used to report something as is. I cannot think of any other usage examples. If you have some from your book, let us know.