yes, if you aren't able to retain sodium bad things will happen.
are you able to handle any sort of dairy in any forms? i.e. raw cow milk, raw goat milk, hard aged cheeses raw or pasteurized, soft cheeses, whey -- raw or processed?
when i was experimenting with sodium years ago it was always the food sources that worked best for me, adding salt to water didn't really cut it.
also, complexing the sodium with foods like adding salt to soup or meat or fats or nuts seemed to work better than just water and salt, why? i have no clue, but it worked. have you gone through many different types of salt? kosher salt, table salt , different types of Sea Salt s, himalayan rock salts pink and black, realsalt from the utah saltbeds. dr. wilson recommends trying a lot of different salts until you find the one that works best for you.
another thing that worked for me was to take in sodium away from water only with foods, and then wait a while until i became thirsty for water.
you mentioned 4 teaspoons was your largest dose, have you ever tried to go beyong that amount? i suppose it is possible that you might need more than that.
if you are completely unable to retain sodium due to that severe an aldosterone problem then you really need to get on that first and foremost before you can do anything else. without sodium your entire electrical system will be fried and crashes will be the norm. i wonder also if your dosing schedule could help, maybe sipping the salt water a bit at a time throughout the day instead of in large quantities all at once.
have you tried bathing in salt water? get 1-2 pounds of Sea Salt and try it in a bath to see if you can absorb it that way. or if you have any access to bathing in an ocean give that a try.
i'm on your side and trying to help. i am well aware of the aldosterone issues, been there done that and corrected it. i never encountered a person who was completely unable to retain sodium though, it sounds more like addisons disease than adrenal fatigue. at one point i was scarfing down giant bags of chips with tons of extra salt added to it. it was amazing how fast things turned around for me after doing this, i could go from dizzy and tired to running up staircases.
good luck with this issue, and try to focus on this issue because it is primary.