I think you could glue the base and then attach if you use a lot of alcohol. So you would put the glue on, let it dry to tacky, then spray the inside of the base generously with alcohol, and also spray your head generously with alcohol, before applying the piece. The alcohol would delay the onset of adhesion, and give you enough time to get the piece into perfect position.
If you try this, be sure to wear a sweatband to stop the alcohol getting in your eyes.