I think it should be strapped down over the battery either way.
Regardless, If trying to adhere plastic to fiberglass, I would use some sort of epoxy.
There are 2-part epoxies you can get from walmart that are pretty strong.
No matter what you use, if you are going to get them to stick, you will need to scuff up the smoother plastic piece first. 36 grit sandpaper on a drill lightly just to created scratches and grooves for the epoxy to bond to. the fiberglass is usually rough enough to bond to (cloth side, not gel-coat side), so just clean it up with acetone.