At the end of "The Angels Take Manhattan", when the Angel sent Rory into the past, Rory's name was on the gravestone & anything they did to change that would cause another paradox that (as the Doctor said) "Would rip New York apart." Once Amy had let the Angel send her back in time & her name was on the gravestone, too, that also applied to her. Because they'd created "fixed time", even visiting them would cause a paradox: "I will never be able to see you again."
No matter where or when the Doctor or River contrived to make the change, the paradox would involve New York, since that is where the gravestone is.
That's why River had to write the Melody Malone book. It was already part of events & failing to write it or to get it published would have been a change that caused a paradox. Even so, as River herself said, she had to send it to Amy, not take it in person.