Same thing happened to me last spring when I opened up for the first time after a full season of just tossing pucks in and not really paying attention to what that was doing over time. I didn't even know CYA accumulated like that until I started reading more, so when I tested and got a number around 90 I had no idea what I was looking at or why it mattered.
The partial drain route is basically what everyone pointed me toward and it did work, just takes planning because you need to know roughly how much water to pull out and replace based on where you're starting. I didn't have a good feel for the math so I ended up doing it in two rounds, pulling down maybe a third, refilling, testing again, then deciding how much more to drain. Probably could have been more efficient about it but it got me from 90 down to around 40 which is where I wanted to be. One thing I'd ask, and maybe someone with more experience can weigh in, is whether there's a meaningful difference between draining from the deep end versus letting the pump pull from the main drain during the process, or if that just doesn't matter much. I've seen it mentioned a couple times but never got a clear answer on it.