He goes "Flipside" around 10:27. Faced with the knowledge he's killed death (as in "Its a Wonderful Afterlife" volume 2 where Robert Thurman does the same) he makes a bucket list of things he wants to do in the afterlife (including eating things in buckets).
He gets into a chariot with his soul group, driven by Santa, a unicorned Abe Lincoln and... Alex Trebek (!) who says about the existential questions of life and death: "All of life's important answers must be in the form of a question." ("Why are we here? Are we really here?")
In the finale, everyone who's ever been in the life of the Colbert Report's sings "We'll meet again" - pretty much the same thing people claim about the afterlife during NDEs, OBEs and LBLs - seeing all your loved ones again in a display of unconditional love and reverie... (except those who are busy elsewhere, like Billo Reilly).
Loved the reference to the ending of Dr. Strangelove, which includes this Flipside tune:
"We'll meet again, don't know where, don't know when. But I know we'll meet again some sunny day. Keep smiling through, just like you always do, Till the blue skies drive the dark clouds far away. So will you please say hello to the folks that I know, tell them I won't be long. They'll be happy to know as you saw me go, I was singing this song. We'll meet again, don't know where, don't know when. But I know we'll meet again some sunny day. Keep smiling through, just like you all ways do."
A fitting end. Colbert Report is dead, but it lives on. Just as we do.