Thats a hard one. Glue does not like to hold a butt joint very well. Mabby some kind of epoxy will work but make sure it is sandable/shapable. I fixed my grill after if broke with some Zap-A-Gap. It is a sandable super glue made just for plastic But I don't think it will work for what yu are doing. If you had some smaller areas that are not butt joints or some cracks, chips, or gaps that needed filled it would work good. One thing that will help the strangth of the butt joint is to put some scrap plastic on the back side of the joint that briges the gap. That will help a lot.