Oh yeah! It was tilted because that’s how it fit into my character. So I took your advice and rotated it to be facing directly forward, then UV unwrapped and edited again, but I got the same result as before! Thanks for still trying to help, I really appreciate it!
Bake Sclera and Bake Iris are centered (Bake Sclera appears to be the one you screencapped earlier), but the active map (UVMap) is not. Image textures in the shader editor (and the UV output on the Texture Coordinate node) default to the active map—you can use the UV Map input node in the shader editor to call on specific maps.