I'm not sure the original premise has much promise, anyway, but I'll try modifying it instead of throwing the whole thing out.
-make the Baku more sympathetic and make them a real civilization of thousands or millions rather than a tiny village of squatters. Have them actually be connected to the planet as their home rather than some place they stumbled upon 300 years ago.
-take Dougherty and the other side's arguments more seriously. Make him convincing and have some of the senior officers side AGAINST Picard, as they probably would if we're being realistic.
-darker tone, less "silliness."(pimples, boob jokes, etc.)
-make the dilemma more balanced by not having the stakes be a revolutionary medical resource that HELPS BILLIONS. Have the resource be something like a new fuel source or something that would help the UFP in the war.