One of the managers at the pool store said the problem with the CYA neutralizer is the formation of crystals that destroy the cartridge filters, and that can't be removed when cleaning the cartridges. I suppose that you could put some sort of pre-filter into the pump basket or skimmer to catch them first.
Amazingly, he also said that he's been telling employees not to be so quick to always push the tri-chlor tablets on everyone because of so many people having cyanuric acid problems, and to recommend liquid chlorine. Even though I drained and refilled just one year ago, my cyanuric acid is up to 60-70 ppm. When it was 120 ppm, it was hopeless to try to prevent the algae without pouring in many many gallons of liquid chlorine, resulting in an uncomfortably high chlorine level, so a drain/refill was required. However they just significantly raised the water rates due to a drought, especially on the higher usage tiers, so a drain/refill would probably cost me $500 now, versus $150 last year.
So I'm swearing off the tablets for a while until the CYA level comes down from simple evaporation and topping off during the summer.
I'm sure the pool stores would _love_ a simple to use CYA neutralizer. They could sell you the tri-chlor tablets and/or the stabilizer, then sell you the neutralizer, and continue this cycle forever. They don't make nearly as much money from the chemicals required after a drain/refill.