The twelve

[Enkidoh]

As Mjollnir stated, the Deity Stones were actually part of 1.0's storyline - specifically they were actually carved by Louisoix as his 'Plan B' in the lead up to the Calamity - using the power of prayer to summoning a portion of the Twelve's collective power to reseal Bahamut (much like how SMNs summon a portion of a Primal's power as an egi) - naturally this didn't quite work as well as it should have. And yes, the final quest for that involved travelling to each stone in turn and praying to it (praying to the stone of your Guardian rewarded you with the ring for that member of the Twelve).

It's not widely known but in ARR there is already a 'stone pilgrimage' trek in the game - as a part of the wedding ceremony quest 'The Ties That Bind', to bless their wedding rings the player is tasked to form a party with their fiance and travel to each stone in turn and, like the aforementioned 'Living on a Prayer' quest in 1.0, with the ring equipped, /pray to the stone, which triggers a short cutscene at each. So the stones already have a connection to ARR's story.