I have a possible solution to the X-Men Origins: Wolverine timeline conundrum.
Maybe Sabertooth killing his superior officer, Wolverine and Sabertooth getting shot by firing squad, coming back to life, getting recruited into Team X, and Wolverine leaving Team X all takes place within the first 6 months or so of 1973, and so for the remainder of the year Wolverine is living on his own in the U.S. when his future self arrives to change history in Days of Future Past. Then "6 years later" it is 1979 and the main events of Origins or some variant thereof occurs in both timelines.
However if we want to synchronize the movies with real-life, then that's going to be difficult since the Paris Peace Accords were signed on the 27th of January 1973 while the Three Mile Island accident occurred on the 28th of March 1979. However, I don't recall seeing any newspapers in the movies with exact dates.
The US was still prepared to use military force in Vietnam (though primarily bombing campaigns) after the Paris Peace Accords if the NVA launched a major offensive into South Vietnam. It wasn't until the Case-Church Amendment later that year in mid-August 1973 that any such action was strictly prohibited due to the unpopularity of continued involvement. And there were still many US military personnel left in South Vietnam until 1975, right up to the fall of Saigon, so there's nothing saying Team-X couldn't have been running around doing off-the-books black ops assassination missions and acting as "advisers" to the ARVN during that time.
Also, judging by the changes made to the backstory of the Cuban Missile Crisis (acting like us having nuclear missiles in Turkey was a new thing inspired by Shaw and weren't already there earlier, for instance) and Three Mile Island, the series has never had any trouble altering historical events to suit its storytelling needs, so there's no reason why we can't fudge the details a bit here too while remaining true to the overall point.