Yes, I see no problem, neither with the typography nor with your analysis. You will see that such block quotations are often used in books.
As an alternative, you could say that he said is a complete sentence. Then the quotation that follows is seen as syntactically independent, the connection being purely semantic.
That would not be my choice, because both the lack of an object to said and the lack of sentence-ending punctuation after it point to a syntactic connection.
Then again, punctuation is only punctuation; and it must be admitted that the use of say with direct (quoted) speech is syntactically different from say with indirect speech (that ...).