The problem is that the game (both Cid, Dysley, and the Datalog) specifically told the party and player that the destruction of Orphan would lead to the "destruction" of Cocoon because Eden would no longer be able to coordinate the Cocoon fal'Cie, leading to humanity's demise, and the entire orb would fall out of the sky (the latter was first mentioned I believe in one of the Datalog entries).

Their focus and whether they successfully defied it or not before fighting Orphan the final time has absolutely zero bearing on the fact that killing Orphan = Eden unable to function = Cocoon fal'Cie can't take care of humans and killing Orphan = Cocoon falls out of the sky.

The party all agreed to "Protect Cocoon!!!11", and protecting Orphan was the exact reason they came back after Oerba...because as far as the party and player had been informed by the game itself, the death of Orphan amounted to exactly the same thing as Cocoon's destruction because of what would happen when Orphan died.

So, in essence, they just decided to kill Orphan because they were finally fed up with all fal'Cie and hoped some solution would present itself later...they had absolutely no plan for what would happen when Orphan died other than "hope" things worked out (the cinematic after the battle suggests Fang and Vanille already "knew something," but this was never mentioned to the party or player anywhere in the game).

Yes, as Croyles points out, defying their focus and becoming free of it enabled them to save Cocoon in the end, but there is no suggestion until the final cinematic that they had any idea how they would do that.

They "hoped" things would work out -- as it happened their "hope" made a miracle happen: the great deus ex Raganarok conveniently bailed out our mighty heroes for doing exactly what they had agreed not to do for some thirty hours previous.