Repair or replace the back cover

So this is pretty incredible. After years of using the Steam Controller regularly, the two top pieces of the back cover finally snapped off, like baby teeth. One of the pieces even ended up inside the controller!

I'm not sure there's any chance I can repair this cover considering this is molded plastic, but is it possible to replace the back cover? As is, the back cover does not sit nicely in the controller. Only the spring-loaded lever at the bottom is holding it in. While it can still cover the batteries, it's very difficult to press the grip buttons with this grip as is without some reinforcement to hold the top of the grip to the back of the controller.