I've reinforced laptop lids and other flat surfaces in the past using carbon-fibre sheet and Araldite, but this is a slightly curved surface and the case is slightly flexible.  I think just running Araldite into the crack will fail, as the mating surface would be just the thickness of the plastic and the slight flexing in use would rapidly crack the adhesive. 

Poking around your videos, I've found the one in which repairs are being made to a kayak, and I can adapt the technique.  But I have one problem: I'd like to be able to get a gloss surface on a slightly concave section, and the technique of stretching release film over the area obviously doesn't work for that?  Is there a technique, or do I need to accept the surface will need to be sanded and re-coated?