To permanently lower TA, you must include aeration into the equation....in other words, manually accelerate the natural tendency to out-gas CO2 out of the water. So as Ms Coffee suggests, the CYA has virtually no affect.
Perhaps even more important, do not overestimate just how much effect CYA has on pH. Use the poolcalculator to set up scenarios but you will find that adding normal amounts of CYA to your pool will not have any really drastic affect on your pH.