1. This film is shooting all the way until October, we don't how long the current cast members are going to be shooting the future scenes nor do we know when the First Class actors are arriving on set, not to mention that Sy's film isn't locked in as starting in May for sure. He could most certainly shoot future scenes, go off do filming for another movie then come back and continue shooting when First Class actors arrive. It's not unheard of for actors to shoot to films at once.
3. Transporting the big characters back in time doesn't really help the future storyline either because there really wouldn't be any point to having scenes in the future if the majority of the characters go back to the 70's which is why is really doesn't make sense to have Magneto, Xavier, Wolverine, Storm, Rogue, Iceman, or Colossus go back in time. Not to mention, transporting them back to the 70's would almost certainly overshadow McAvoy, Fassbender, Lawrence, and Hoult, which most certainly won't happen.
3. Saying this is more of an X4 than First Class sequel is inaccurate since we've been told repeatedly the majority of the movie takes place in 1973 which cuts to the future.
What I'm getting at is that if we are to believe Singer when he says that EVERY character has a point and is needed in the story and plot, knowing Bishop is in this most certainly makes in the biggest candidate for being one of the time travelers. With his connection to time travel in the comics and television series, it really makes logical sense and there really would be any point in just making him a character in the future storyline. If you add in Blink to that, where they can most certainly tweak her powers a bit and make her portals time jumping the pieces just fall into place.
That way, you keep the the original cast in the future where the story can solely focus on that team and then you have the First Class actors where they story can slowly focus on them with out either team being overshadowed by one or the either and each characters plays their part.
Of course, this is just my speculation on things.