As others mentioned, if fish are moved at all, it should only be to adjacent or nearby watersheds. However, what's to keep the transported fish in the river it is transported to? It will recognize its new environment as the wrong river and very likely drop downstream, even into the ocean, to resume the search for its home river. Some fish transported this way will accept the new home and spawn there, but most probably won't.
This technique was actually done with chinook salmon that tried to return above Grand Coulee Dam on the Columbia River during project construction. The fisheries people ended up constructing a weir on Nason Creek, a tributary of the Wenatchee River, to force the chinook to stay there and spawn, as it was their nature to try to drop downstream and seek their natal waters upstream of Grand Coulee.
Another possibility, although not extremely productive, would be to take such excess natives from a healthy population and spawn them, artificially incubate the eggs, or plant them as eyed eggs in selected tributary streams, or stock the steelhead fry in selected streams. Fry stocking that adheres to a strict protocol can yield smolt production of about 2 to 3% of the number of fry stocked.
If possible, I think the best way to recover a run is to relax the harvest pressures on it and let the remaining population bounce back in a cycle or two. But if there are few or no natural spawners remaining, then TM's suggestion with suitable modifications, has merit.
Sincerely,
Salmo g.