There are other ways to deal with high CYA pools, but they involve extra expense using algaecides and other products. If one absolutely cannot (or is unwilling to) dilute the water or maintain a higher FC relative to the CYA level, then one can use PolyQuat 60 weekly both to control algae and as a mild clarifier (which you need because the lower active chlorine level breaks down organics more slowly). It still won't prevent algae if the chlorine gets to zero, but the FC level doesn't have to be as high as it otherwise would. Of course, this is extra cost -- usually around $2-4 weekly (after a larger initial dose) depending on the size of the pool.

I know that in my own pool years ago (before visiting this forum) when I was initially using Trichlor pucks/tabs I was also using algaecide, but every other week. My pool "turned" somewhere around 3 ppm FC with 150 ppm CYA. If I had been using the algaecide weekly then perhaps I could have gone to around 200-250 ppm CYA again with 3 ppm FC. So very roughly speaking, the algaecide may lower the minimum FC level from the 5-7.5% of CYA range to the 1-2% range, but that's really pushing it. You still have the problem that IF your pool gets behind the algae curve, then it still takes a very high level of chlorine to get rid of the algae since shocking the pool will tend to get rid of the algaecide more quickly so you're relying on the chlorine to get rid of the algae.

Yet another option is the use of 50 ppm Borates, but we don't have enough data to know how much it prevents algae growth. We know that it does as we've had multiple reports about that and I have it in my own pool now and have done some experiments, but my hunch is that it's not better than PolyQuat, but not that much worse either -- so a total guess on my part is that it would allow for something in the 3-4% FC as a proportion of CYA range, but I don't know exactly where in that range.

There are other options, but they have side effects or are not always effective. Copper-based algaecides kill algae, but can stain pool surfaces. Phosphate removers take the edge off of algae growth, but don't help if there are organic phosphates in the water, especially if the chlorine gets to zero at which point bacteria can quickly convert organic phosphates into orthophosphate.