Thank you for the additional information.
I ask about other medical problems because low sodium (hyponatremia) is commonly due to other medical problems that affect fluid and sodium status, such as congestive heart failure or significant liver or kidney dysfunction. There are other possible medical causes of hyponatremia, such as hormonal problems involving ADH or thyroid
disease. It is also possible to develop hyponatremia because of excessive intake of fluid. With the amount of fluid that you are drinking and since no other medical problems have been identified, then the underlying cause of the hyponatremia would be the excessive fluid intake.
In this situation, the usual treatment is fluid restriction. It is usually not effective to increase sodium intake. It has to do with how the body, and particularly the kidneys, handle excessive amounts of fluids. There is a limit to the amount of excessive fluid that can be cleared from the kidneys, so that excessive drinking will lead to accumulation of the excessive fluid, diluting the amount of sodium in the body.
You can try to increase salt intake in foods and fluids along with a moderate decrease in fluid intake to see if a balance can be created. But from a medical perspective, it would usually be better to perform a more significant fluid restriction initially (about one quart per day), and then after the sodium is corrected, there can be an attempt to allow for more fluid along with a greater amount of salt to try to maintain balance.
Regardless of how you are trying to correct the blood sodium, it is important to monitor the sodium closely because a sodium level of 127 is quite low and is approaching the threshold that is considered to be severe (a level < 125).
If you have any further questions, please let me know.