Where did you hear she was contracted to do a “2nd draft and a polish”?
Gary Kurtz and Lawrence Kasdan both said at different times. Kurtz in Starlog before they started shooting Empire in 1978 or near to that. And Kasdan when he was promoting his documentary last year or the year before.
There is some mention of it this thread from 2010 here: Leigh Brackett’s first draft of Empire
I think Gary Kurtz also mentioned in in a much later video interview he did, and also in a book, “Secrets Of The Force”.