It should be noted that Marcia Lucas herself, in "Howard Kazanjian: A Life" by J.W. Rinzler, seems to suggest that the idea of a "time limit" might have been, or actually was, fellow editor Paul Hirsch's idea. Her memory seems a bit hazy. I believe Paul Hirsch agrees in his own book that it was his idea, but I don't own a copy of it, so someone would have to check me on that.
However, this was simply an ADDITIONAL time limit. The Death Star was always going to be slowly approaching the Yavin moon in order to destroy it. As we can see as early as the January 1976 version of the fourth draft, from well before the editors had the above discussion (notice Ben Kenobi is even still alive on Yavin), the princess sits in a control room with generals watching a "giant display" depicting the Death Star as a "red dot" that "moves ever closer to the system." We see this display in the movie, still playing a major role in creating tension.
That story about how the whole concept that the Death Star was about to destroy the rebel base was created in editing is wild.