If you don't have experience with hide glue, the contact glue is a pretty good option, since these are relatively thick pieces and won't be affected by your finish. After the glue is dry to the touch it would be a good idea to put dowels between the pieces to keep the two glued surfaces from making contact until you get it centered.
Mike, an American living in Norway
Theory is when one knows everything, but nothing comes out right.
Experience is when everything comes out right, but no one knows why
In my shop theory and practice are united. Nothing comes out right and nobody knows why.