broken shower pan
Doesn't sound like something you should consider installing. I'd get a new pan....Why risk it?
No, there's no way that I know of to incorporate a membrane into a molded shower pan drain, and any membrane needs to be pre-sloped to the drain (even if there were a way to tie it into the drain). Placing the preformed pan over a sloped mudbed would certainly not work because the pan would easily deflect.
Do yourself a favor and throw it away and get a new one. The costs of doing that are small compared to repairing moisture damage down the road.