The thing is, the Hydra is already dead. I don't think there is anything they can do with the Hydra cause in the 2nd act of the film (with elements of it being used in KH2), Hercules managed to kill the Hydra (including most of its heads) by creating a rockslide burying all of its heads one by one in a pile of huge rocks and in Kingdom Hearts II Sora managed to vanquish all of its heads with his Keyblade with some help from Donald, Goofy, Pegasus, Phil, Megara and Pegasus.
This is a very good summarization of the plotline to Olympus and part of it is actually what I envisioned how the world. In regards, to the world starting off with the Rock Titan battle, I dunno, sure, in Dream Drop Distance Ursula was the first boss at the start of the game, but frankly, it just feels to soon to have it happen right after the Young Xehanort/Young Eraqus scene. Perhaps the world begins as you said Sora training with Phil on Phil's Island or in the grassy areas around Mt. Olympus (as shown in the E3 2015 trailer).
The only thing that remains is Megara's role in Olympus in Kingdom Hearts III and whether it would be reminiscent to her role in the film's climax when she sacrifices herself to save Herc from a falling pillar. Because elements of the scene when Hercules sacrificed himself to save Meg and becoming a God for his selfless act was already used in Kingdom Hearts II, so I don't know if the team will do the same thing again, but who's to say?