Replace Late 2013 Logic Board with Mid 2015 15" MBP
I don't think they changed much from year-to-year until the Touch Bar came out. Is it possible to put in a Mid 2015 logic board into a Late 2013? I know it's possible for 13" in this same set of years.
On an earlier machine, I was able to upgrade the LCD to a new one that wasn't available when the original model shipped.