What is the only non-drain method that actually removes cyanuric acid from a pool?

Reverse osmosis is your only real non-drain option. It costs a few hundred bucks but strips out CYA, calcium, and other dissolved solids without dumping half the pool. Everything else — CYA reducers, bacteria treatments, or dilution — is either unproven or too slow to matter. For most people, draining a third of the pool and refilling is cheaper and easier, but RO is worth it if the quote isn’t crazy.