@ninetyfive for what it's worth, I had the same problem. Here's how I repaired it:
Mix 50% baking soda and 50% graphite powder. Graphite powder can be made by splitting open a standard wooden pencil and grinding the graphite stick against sand paper into powder.
Mask the front (or visible side) of the cover. You will be working on the back side.
Use a popsicle stick or really small spoon to put the powder in between the crack. Do try to work some of the powder in between the crack. The masking tape help it from falling through completely.
Drip CA glue over the powdered crack. CA glue is just super glue or krazy glue. Don't use the gel stuff. The thin glue works best. This chemical reaction with the glue will heat up the plastic kind of like how ABS pipe cement does.
It will dry quickly and you will probably have a messy lumpy seam, but this is only the backside.
Now to smoothen it out. Use a cheap low powered soldering iron with a flat tip. I used a Modifi3d finishing tool that's used to correct plastic 3d prints. Heed this warning: The fumes are awful. There will be a lot of white smoke. Don't breath it and don't get it in your eyes or it will burn. I did this over a gas range hood that was extracting the fumes. Don't put your face over the fumes. Use the tool to smooth the seams.
Remove the masking tape. It does show a bit of a seam on the front side, but the chemically welded joint is stronger than the rest of the plastic.
This is my go-to method for fixing cracked plastic. The basic procedure (minus ironing the plastic with a soldering iron) can be viewed on youtube: