It is ashame. Hybrids would most definitely help reduce numbers of shad and would also attract more fisherman to that lake. But there has got to be another viable solution to ridding or decreasing numbers of shad without stocking another non-native species. Hybrids are sterile and can't reproduce so with time they would die off, so that's not a long-term concern to Ecologists and Fisheries Biologists.
This is just an idea, how effective would drawing the lake down substantially work? Shad are a fragile fish species and with a low oxygen content and being over crowded, I could see many dying off. A draw-down would also make it easier for the fish and boat commission to set trap nets intended to trap the shad and remove them. Problems with that is $$$ and possibly killing other fish. Idk, just a thought.
Last solution is completely draining the lake, removing all* fish, transporting the desired ones to other local lakes, and starting that lake over from scratch. I think that's the only way to really do it, but I don't think that would fly. Too many anglers would hate that