If you want to have a chance with CYA that high you need to be diligent with FC being kept above min at all times, try to stay within the target range:
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Once you have algae, you will not get rid of it by maintaining target FC, you will have to follow the
SLAM Process. And this is a challenge at CYA 100:
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You'd be better of draining some water to reduce CYA should you have to SLAM. Especially with your limited access to test reagents.
High CYA is not reducing FC as such. The problem with high CYA is that high FC levels are required to actually have a sufficiently high amount of hypochlorous acid (HOCl), which is the form of FC that is actually sanitizing your pool and killing algae - the rest of what shows up as FC is less efficient hypochlorite ion and absolutely non-sanitising chlorinated cyanurate (i.e. chlorine attached to CYA, that's your reservoir of UV-protected chlorine that still shows up as FC, but has no sanitising or oxidising powers).
Once FC is too low, algae creeps in and creates additional chlorine demand, which can be huge. I suspect that's what you are dealing with.
An
Overnight Chlorine Loss Test would be a good starting point from here to assess the situation.