That's a very good question.  Since the meteorite plot point is on the horizon, we'll need to decide this sooner rather than later.  If we're going back to Kanto for the Battle Frontier, it would make more sense for Pyramid King Brandon to have the Regis (for now).  This leaves Groudon and Rayquaza.

For the fossils, since there's only two to be found in the desert and the group has practically become a trio now, one of us would miss out.  I don't mind if it's me.