Uses for Souls

Man, your game sounds awesome. I'm jealous, user.

In my head canon a soul is a tightly bound bundle of planar fabrics. Good souls have energies of the celestial planes and evil souls have energies of the fiendish planes. Most souls are neutral and have fiery and other elemental energies. This artifact could potentially be used to create a new demiplane or perhaps even a major plane of existence. But why would you want to do that?

It is extremely difficult to become a planar lord and to become so bound and wreathed with the fabric of a plane that one is tied to it. There are many demon lords, archdevils, archomentals, abyssal lords, celestial paragons, etc... Typically, these mighty powers rule unopposed or underneath a greater lord. However, if you were to create your own major plane you could become bound to it and rule freely without opposition. You would have the power of an archdevil and etc... and yet rule without the laws of such a place.

Now it is possible to create your plane inside the Ethereal plane or the Astral plane but I would submit a better choice would be to create your plane inside the Far Realms and rule freely without subjugation underneath an Overgod.

Would it be cooler or lamer if I said that this is the first campaign that my DM has ever run? And that we're only 3rd level so far.

A little lamer, but only because it means the ideas presented, although good, are probably not as fulfilled as they could be with a more experienced GM/Group. Still, for a first game, it still sounds pretty good

I saw the idea of communicating with the souls. If you can, and they retain memories, you could filter through them to see if the possess notable skills/knowledge, and leverage them into teaching you.

Build a massive flying castle, plug the stone into the central core. Rule the world from your celestial palace, raining fire and lightning upon any who would oppose you in your grand and mad ambitions.

Become god-kings of the universe, release so much magic into the atmosphere that it becomes a high-fantasy setting, and damn the consequences. Immortality is only the first step! You have so much power in your hands that the difference between your party of adventurers and a pantheon of gods is only academic, at best.

Use the stone. Change the world.

This.
Simple plans are the best plans.