What is the only reliable way to lower cyanuric acid in a pool?

Partial drain and refill. You have to physically remove water and replace it with fresh water because CYA doesn’t evaporate, break down from sunlight, or get destroyed by chemicals. Drain enough to dilute CYA to your target (e.g., drain 66% if CYA is 120 and target is 40), then refill and retest. To avoid this, stop using stabilized chlorine and switch to liquid chlorine or cal-hypo.