errr i really don't want to be that guy, as you surely got some great skill

however, you should start your projects with 1024x512, so the mapping will look correct

i mean look, you did amazing job, the only real complaint i can give is the the aspect ratio when the head is on sphere , as if you noticed it looks deformed, which is a result of making the texture on 512x512 instead of 1024x512 and then scaling it to 512 square

so in order to fix it you will probably have to redraw it and it is too late for that, but i hope this advice will help you with your next head textures