Who

was it that eventually convinced people that the fixed stars aren't on a sphere?

That was the french philosopher rene de carte. He's the i think, therefore i am guy. And in the mid 16 hundred just after galileo's death, he published his own theory of the universe, which became very popular. Now, he didn't generally pay much attention anything aristotle said, but he did agree with aristotle that a vacuum, or empty space cannot exist. As a result, he thought the universe is filled with matter, and that matter is obviously moving, as the planets indicate. But if the universe is completely filled up with matter, the only way for one piece of matter to move as if the piece of matter in front of it also moves. And so descartes conceived of our solar system as a big swirling vortex made out of matter with the sun at the center. He also thought of the earth as being at the center of its own vortex as it went around the sun. And the moon was trapped on the edge of the earth's vortex, like something going around the edge of a whirlpool. And descartes thought of the stars as distant suns at the centr of their own vortices. So for from descartes, the idea of the stars as distant suns took off. He's the one who popularized that idea. There had been speculation about this idea in antiquity, butt was his vortex based cosmology that popularized it. An article on the library of congress's web page explained,

in descarte's system, like aristotle's, the universe was full of matter.