Sorry to take so long to reply.
My pool is now very clear! Yay!

And I'm pleased to report that I didn't spend a dime to do it, either.

I tried an old trick I used a couple of years ago to get rust-red out of the high-iron water we have: Old towels in the bottom of the skimmer basket. They seem to filter out even the smallest of particles. I changed them out morning and evening, and after about 5 days, super clear water.

Boom.