advice replacing small roof section of wood

Before you put the new section in, maybe you could use pieces of wood to go under the edge of the existing panel. Glue them and slip them in and clamp and shoot will a staple gun. When they are dry you can lay the patch in and the edges will be supported. These supports would fit between the roof rafters.

I have used the loctite pl premium adhesive from the depot with good results. I would stay with the premium or sub floor type adhesives.