Frist, the difference in your CYA readings is from operator testing error. NO doubt in my mind about that! There is NO way that taking your solar cover off and adding baking soda (which is what sodium hydrogen carbonate is) will lower your CYA! The CYA test is the easiest to get bad results from sloppy testing. Get a test kit and test it yourself!
Second, Total alkilinity vs. ajusted Total Alkaliniy....The amount of CYA in the water will have an effect on the alkalinity reading. The CYA will show up in the TA test and make it read higher (your Ph at the time of testing will have an effect on this and possibly on the TA reading also). If you CYA levels are very high this can cause your TA to read a bit higher than it actually is for a giving pH (higher than the actual amount of carbonates/bicarbonates in the water). Many people don't feel this correction is really important. IMHO, unless your CYA levels are very high and your TA is at the very low end of the accepted range it really isn't that important as your own numbers show the trend. If your CYA is in the accecpted range of 30-50 ppm this correction has very little impact on the TA reading for a given pH. Also get your pH in line first since this has an effect on both the TA and adjusted TA as you saw in your own research!
Just decide if you want to use TA or adjusted TA and stick with it once everything else is in line. I personally just use TA on my own pool because I am too lazy to do the math and my numbers are still in range when I make the correction! I think you will find the same to be true once you get everything balanced.
My advice would be to lower the CYA by a partial drain and refill and then retest. Also, get a good test kit and start doing your own testing. It's really easy.
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