FFIV: TAY connects I-VI, as does Tactics and I-VII

Ivalice connects Tactics to XII

The official thingy connects VII and X. IX has 5 billion references to the other games.

So all the main series except VIII and XI are already connected to each other. I have no idea about XI, but VIII is a singularity and I'm a mathematician so I remove it and everything works out. Q.E.D.