Re: In the books, "the future" was 2013!
Do the Mutant Control Act (or equivalent) take place in 2012-ish, after the events regarding "the cure." Show that the cure had no permanent effects, as was hinted at the end of TLS. This movie starts in 2032, 20 or so years after the Act is put into effect.
You get an exceptionally elderly but powerful Magneto and Xavier and a weathered, but still effective Logan. This also allows enough time for sentinels to be constructed, the MCA to be in full effect, many of the more known mutants to have passed and the world to begin to crumble.