Gillnets ARE the answer if you're looking for an essentially unregulated fishery.
Live trapping is definitely the answer if you're looking for healthy, self-sustaining runs of varied stocks of fish. Every fish trapped could be typed as to its origin, so harvest criteria could be applied at time of capture. Fish from threatened or endangered stocks could be released back into the river and the harvestable fish could be bonked and sold.
It seems so simple.
Gill netters could form syndicates, I suppose, to build fish traps cooperatively on the lower river. The same with the gillnetting tribes upriver.
For that matter, fish could be harvested easily with dip nets at the fish ladders, and the same harvest/no harvest criteria applied to each fish dipped up.
Too easy to regulate; that's the big drawback.