I have brined enhanced birds using a strong brine and it seemed to take. As you mentioned, a weaker brine is just wasting time.
As for drawing out salt using water, I have a thought about that (not facts, just a thought). It might draw out some excess salt, but I am thinking that if some of the molecules of salt and water truly are "trapped" in the strands of proteins, then those would not come up from a soak. It will be interesting to see what you come up with for sure.
Thanks for sharing, and keep us posted!