Hi there! I'm not sure there's a way to remove the headrest. However from your picture, it appears something is in the way preventing the seat from going down further. Make sure there's nothing under the seat part, and nothing under the part your back is against. Mine lay down completely flat when nothing is in the way.

Hello i have a also have a 2003 chevy trailblazer and no i dont think there is a way to make the seats flat You can try moving the front seats forward a little but i am unsure if this will work or not and the driving experience will be altered

I know i’m super late but uh... you forgot to lift up the base part of the seat. before laying the seats down you have to lift up a strap that’s in between the seats so you can lift up the part of the seat where you sit then you put down the top part. if that doesn’t work try moving your front seats up.