First, it take a very high concentration of salt for there to be undissolved salts. If you can collect the white powder, put it in a cup (not styrofoam) with some water, then add some muriatic acid. If it bubbles up and dissolves, it's calcium based. If not, it may be silica based.
Second, Water Balance is most important, and not any one parameter moreso than another.
Third, calcium hardness in Arizona usually comes out of the tap at around 150 - 200 ppm. Not high at all. However, due to the amount of evporation, your make up water is continually adding more calcium hardness, so that over time, your calcium hardness level rises to very high levels. Using the Saturation Index as your guideline, adjust your Total Alkalinity and pH levels to compensate for high Calcium Hardness levels.
Fourth, while the comment was made that it does not "keep up with the chlorine demand a shock process requires", it may not generate a breakpoint or superchlorination residual level IN THE POOL, but is certainly able to maintaining chlorine levels and do a great job at controlling chloramine levels, in most situations. And in some conditions, the BOOST cycle is enough to clear up a pool after a pool party.
Finally, to the OP, the white powder may be as a result of very high TDS, total dissolved solids.