I am pretty sure that there is a special trope for the very, very end of the Torah. However, I cannot find it. I need to know by tomorrow so please answer! Thanks!
I'm pretty sure that the end of the Torah is sung the same as the end of any of the other four Books of the Torah, with an embellished style that leads into the congregation blessing "Chazak Chazak Venitchazek". For one example of how this sounds, listen to the end of this recording of the last section of the Torah by R' Jeremy Wieder.
Binder suggests using the Chazak Chazak melody (aka the Song of the Sea melody). i'm pretty sure Jacobson has the unique melody some people do, but that book is 1000 pages long and I don't have it with me right now. Somebody else who has it could definitely find the page and scan it for you.
According to Pinchas Spiro. A very similar niggun to the introductory verses for the Hakafot