CYA does not break down or mysteriously leave, generally. You either have to dilute to get rid of it--if your CYA is 100, you have to dump 50% of your water to get it to 50--or take the "nuclear option"--which you don't want.

You have to let your pool turn into a swamp, full of algae, frogs, mosquitoes, etc. for a month or two, then clean it up. That will consume the CYA, but leaves you with a nasty mess, algae and lots of ammonia in the water. Definitely not worth it!