@SallyD
Let's just summarize a few things here:
1. You're using softened water as your fill water. What is softened water? Well, hard water is high in calcium (Ca) and (Mg) and relatively low in (Na). Softened water is water that has had most of the Ca and Mg ions knocked out and replaced with Na ions.
2. Total Dissolved Solids is the sum total of the concentrations of all of the dissolved ions that are in the water. The main cations in water chemistry are Ca, Mg, Na and Potassium (K) but there can be others such as Manganese, Iron and others. The main anions in water chemistry are Bicarbonate (HCO3), Carbonate (CO3), Chloride (Cl), and Sulfate (SO4) but there can be lots of other minor players like Bromine (Br) and Borate (BO3). To calculate TDS, a lab would measure all of these concentrations and add them up or they could evaporate a certain amount of the water and weigh the chemical residue that gets left behind when the water has completely dried.
3. Your system's TDS sensor cannot measure TDS in either of these ways so it is almost assuredly measuring electrical conductivity of the water and then multiplying that number by a conversion factor to estimate TDS. This is a crude way of determining TDS. There is a correlation between EC and TDS in water but it's not a particularly strong one. The fact is though, the more solutes you dissolve in the water, the higher the EC will go and consequently your system's TDS meter will detect higher TDS
4. You do not know what the chemistry and what the TDS of the water you're starting with before you start adding salt and pool chemicals to it. Well, if your fill water is already high in TDS, you wouldn't have to add a lot more chemicals to it to get your TDS level to rise too high for your Tub's system to handle. Based on where you're living, I wouldn't be surprised to see the TDS of your fill water is high to begin with. That's just based on what I know of the geology and geological history of that region of the continent.
5. You say you initially have to pound your water with a lot of pH-Minus to get the pH under control. That says to me like your water might be high in bicarbonate which would mean the Total Alkalinity (TA) is high. High TA goes with high hardness so that makes sense. Dry acid is Sodium Bisuphate so that means you're adding more Na and more SO4 to the water, thereby increasing TDS even more. As another poster already suggested, stop doing this and start using Muriatic acid instead.
6. Then, after you add all those solutes to the water, you then add other things, particularly salt, NaCl. More Na and now Cl in the water. TDS increases even more. For a saltwater system you need to have a fairly high concentration of Cl so the zapper can turn it into FC. But how high was your Cl concentration to begin with? You need to know because that will tell you how much salt you actually need to add to get to the correct initial Cl concentration to start and run your saltwater system. The problem you seem to be having is that your TDS is already very high to begin with before you start adding salt. You then only need to add a little salt to get your TDS level up to where your TDS system thinks it should be but the TDS is made up of other ions and doesn't have enough Cl for your salt system to work properly. This is why your tests show your salt is low even though your TDS is high.
So I think the only way we can figure out the best way for you to manage your water chemistry we need to find out what the chemistry is of your fill water and it wouldn't hurt to also find out what the chemistry is of your water is before it gets modified by the softener. Once we know these things, we can figure out a way for you to get your tub water ready without sending the TDS level through the roof, or maybe we'll just find out that you can't use that salt system with your water because it's just too high in TDS to start with.
First of all, is it well water or city water you're dealing with? If it's well water I would fill up clean 500 ml plastic bottles with samples of your water before and after the softener and run them over to a lab to have a Routine Water analysis done on them. If it's city water, I would call the water works department and ask for a copy of the latest water chemical analysis. They do that testing all the time and will usually provide that information to anyone in the public who asks for it. My city publishes their latest test results on their website. That would give you the chemistry of the water you're putting into the softener. I would then get an analysis done of the water coming out of the softener so we can see what the difference is. We may find out that it would be better to use the unsoftened water as fill water or maybe fill with both types.
If you do get this testing done, ask the lab to provide the results in mg/L and not grains per gallon. Those are the dumbest units ever! It will be much easier to understand and work with the data if the results are provided in mg/L.
If you are using City water, it may be that their water is harder and has higher TA and TDS in the winter vs in the spring and summer. This is because the water gets diluted with low mineral content rainwater and snow runoff in the spring and summer. If you can get your system down to where you only have to do fresh fills once or twice a year, you could time them so as to avoid filling with higher TDS winter water.