For some reason, the game loves to throw uber magikarp at me...
I had just arrived in Sootopolis City when the dexnav suddenly detected a magikarp with at least 3 perfect IVs. I caught it and I'm probably going to offer it up for trade.
After the magikarp, I ran into Steven and Wallace, who took me to the Cave of Origin. After a cutscene, I went into the depths of the cave to capture Kyogre. Afterwards, I received the Eon Flute.
Then I put my team, save for crawdaunt and latias, in the pc and withdrew my trapinch, wailmer, relicanth, and my aegislash that I traded over from Y. I then fought all the trainers on the way to Pacifidlog in an attempt to level up and evolve wailmer so I could unlock the Regi trio when I reached route 134. However, then I realized how painfully long it takes just to level up a wailmer. (It's almost as painful as leveling up a larvesta...)
So after entering Pacifidlog, I put the current team, save for wailmer and crawdaunt, in the PC and withdrew my old team. Then I used the Eon Flute for the first time.
Within the next 24 hours after that moment, I caught Uxie, Mesprit, Heatran, Terrakion, and Cobalion. And I found both a Mirage Island and a Mirage Cave, where I caught a Porygon, Purugly, Onix, Excadrill, Klink, and two Tynamo.