In some respects they are lucky they can use conventional...

In some respects they are lucky they can use conventional equipment. But intuitively a lake that does not allow conventional equipment would seem a better candidate for brine recovery from shallow trenches.
Have you compared photographs of the surfaces of Lake Way and Lake Disappointment. The former is brown and the water table always looks well below the surface. The latter is crusted in salt and the water table is just below the surface.
One of those photos in the SO4 quarterly shows the water level down by well over a metre.
Presumably the lower water level and "pre-soaking" are related in some way.