I have a sort of movie treatment for Days of Future Past. It's a little convoluted but I think it works out pretty well.
Skip to the end for the short version. Read the long version for explanations and implications.
The movie begins at some point after X-Men: The Last Stand. The cure is widely available and mutant-human peace has been reached with the help of mutant ambassador Hank McCoy. Magneto, on the other hand, is not so happy. His best friend/rival is dead, he feels impotent without his full powers, and worst of all, mutants are now being considered equal to humans, not superior like he believes they should be. He finds a mutant, Forge, who believes in his cause. Forge has invented a machine which allows someone's mind to occupy their body in the past. Magneto uses this to send Mystique (he could go back himself but I don't find that as interesting) back into her 1960s body to help trigger an event that will draw out the divide between mutants and humans forever.
What event the writers would decide to use is anyone's guess, but let's go with the Kennedy Assassination for now. In this new past, Mystique convinces Magneto that they should teach humans a lesson for taking all the credit and not acknowledging the superiority of mutant powers which ultimately prevented nuclear war. They carry out the assassination on JFK: Magneto uses his powers to guide the bullet while Mystique "gets caught" disguised as an X-Man, thus leading humans to blame the X-Men for this tragedy. This in turn leads to the mutant oppression where sentinels are mass produced to hunt down and eliminate the mutant species.
Now in this new timeline anything that occurred in X1-3 essentially does not matter, and yet they didn't have to outright forget the films because the movie will have begun in the X1-3 timeline thus acknowledging all the events that occurred in those films. This means that in the new timeline they can fast forward to the dystopian future and use ANYONE who wants to reprise their roles from X1-3 to fight the sentinels, and for anyone who does not come back, their characters can be assumed dead (they can even show a graveyard scene with their tombstones).
So in this new future the last remaining mutants have banded together to survive. Forge is now a "good guy" who CAN invent his machine but hasn't thought of it yet. It turns out Magneto was one of the first few mutants captured and put into an internment camp. The mutants find him and free him, at which point he reveals the truth about how these events came to be. Forge then (re)creates his machine allowing the mutants to send somebody back to the past to prevent the Brotherhood from carrying out and framing the assassination. For plot-hole purposes, Mystique should have died at some point in this future, otherwise she could possibly go back a second time. Similarly, Magneto would probably have to die before the machine is invented so he can't go back and just not carry out the assassination
Who do the mutants send back to prevent Magneto from assassinating JFK? At this point, it probably doesn't even matter, although it's a perfect opportunity to introduce a new character (or reintroduce an X1-3 character) into the First Class cast. The rest of the movie (should be at least a third of the overall movie, maybe even half) would occur in the 1960's in a new third timeline. In this timeline, there would be a battle between the X-Men and the Brotherhood where the X-Men succeed in preventing Magneto from getting anywhere near JFK. However, what they did not know and therefore could not prevent was the fact that Lee Harvey Oswald, a human, would carry out the assassination anyway as he was preparing to do originally before Magneto changed the past.
Now, only having introduced one new plot-intensive character (Forge), we have made a movie loosely (yes I know, very loosely) based off Days of Future Past which serves as a sequel to First Class while still acknowledging the original X-Men trilogy, but allowing future sequels with the First Class cast to have complete creative freedom with the story.
SHORT VERSION:
X-Men Trilogy timeline (2013?):
Post-X3 Magneto seeks revenge on humans. He finds a mutant named Forge.
Magneto uses one of Forge's inventions to send Mystique's mind into her 1960's body.
First Class / Dystopian timeline (1963-20xx):
Mystique convinces 1960's Magneto to assassinate JFK and frame it on the X-Men.
Mutants are blamed for the JFK assassination, leading to the mutant oppression.
FAST FORWARD: The last few mutants struggle to fight off the onslaught of sentinels.
Magneto is found held captive in an internment camp and is rescued by the mutants.
Magneto reveals the truth about what he did to change the future, dying shortly after.
Forge invents his machine and sends a mutant back to the 1960's to stop Magneto.
New First Class timeline (1963):
The time-traveler goes and tells the X-Men what Magneto plans to do.
The X-Men and the Brotherhood have a long epic battle as they always do.
The X-Men prevent Magneto from assassinating JFK and having it blamed on them.
JFK is assassinated anyway, but by Lee Harvey Oswald just as history tells it.