Hi Bob,
I did exactly that with my tragkorb lids, although it was in a different area well within the main lid, in the bottom leading corners.
I used a soldering iron with a chisel tip, and waited until it was very hot, using gravity to help I melted the case, directly on the cracks, on the inside surface, and let the plastic "pool" back into the crack. with a bit of help from the hot iron. The results didn't look very pretty as the ABS will harden very quickly away from the heat, but it hardens sufficiently to be rubbed down with a bit of "wet'n dry" paper (done gently, otherwise it gets hot again).
I don't know if there was any deformation or discolouring on the outside surfaces, as they sit behind the applied rubber trim, but I now have two leak free tragkorbs which look fine .. . on the outside anyway.
I have no idea if this would work on the area you have to fix, if nothing else you could stop the crack lengthening by applying heat to the ends of the crack. I would also consider using some support on the reverse side whilst you carry out this fix. It is also very likely that you may have to do both sides.
All the best,
Nickh