There is no record whatsoever of Lincoln using any influence of his office to try to get the 13th passed. None. That's according to the preeminent Lincoln scholar at Harvard.
Here is another REAL quote from the guy you call the "preeminent Lincoln scholar at Harvard". From page 504 of David Herbert Donald's book Lincoln,the book and author you keep using as a source.
He shows Lincoln was pushing the 13th amendment at his party's convention prior to his re election.
https://books.google.com/books?id=fuTY3mxs9awC&pg=PA504&lpg=PA545#v=onepage&q=Amendment&f=false