So far, since June 15, I have used about 35 gallons of 12.5% liquid chlorine and about 3/4 gallon of MA. I used dry acid for the first 2 months and put in about 10 pounds of that. I do not add other chemicals. I did dump about ⅓ of the pool volume a few months ago to reduce the CH from 350 to 200.
Thanks for sharing those numbers. I just put these into chem geek's PoolEquations spreadsheet to calculate the effect on TDS. The effects are:
35 gal of 12.5% LQ: 800ppm TDS (PoolMath says 700ppm)
3/4 gal of MA: 30ppm TDS
10 pounds of dry acid: 100ppm TDS
So, with the TDS of 86ppm of your fill water that adds up to pretty much 1000ppm. You dumped 1/3 of water after a couple of months and replaced that with 86ppm TDS fill water. But I assume you will also have considerable evaporation losses (heated water in an A/C environment, I assume), here you replace basically 0ppm TDS evaporated water with 86ppm TDS fill water, so that will account to a steady TDS increase over time. On the other hand, you will probably also have some splashing losses (your's is a therapy pool, right? - so probably not as much splashing as in a backyard pool), that lead to a TDS reduction.
So, exact TDS increase is hard to quantify, but 1000ppm doesn't sound unreasonable.
As others have mentioned, SWG pools run above 3000ppm, my one runs between 4000 and 5000ppm (Aussie SWGs are designed for a higher salt range). I still hardly notice the slightly salty taste.
I don't see a concern with a bit of salt in the water that would require dumping the water, unless there are legal TDS requirements for a therapy pool (does that make it a commercial pool?).
As James suggested, getting a SWG could be an option once you get above 3000ppm. Since you operate your pool without CYA, you could consider an ORP based automated system (no idea how reliable those are...). Bit of an investment, but it adds a lot of convenience, and you don't have to add LC anymore (apart from the occasional manual adjustment dosage) which will stop a lot of the salt increase. And most people here with a SWG find that the salt makes the water feel more enjoyable - might actually be just the thing for a therapy pool...