So I conclude that the Deadpool movies and the world they inhabit is actually the semi-fictionalized world of the X-Men comics that exist within the real world of the X-Men/Wolverine movies.
As such, it has been really difficult to explain how Deadpool and the upcoming Deadpool 2 fit into the overall X-Men timeline.
That would explain an awful lot about Deadpool and how it can possibly exist in the already established X-Men timeline.
Reddit user DToccs posted his theory about the Deadpool timeline to the Fan Theories subreddit.