Your FC burn rate with cold water will likely be glacial (very slow) as long as nothing is fighting the chlorine in the pool. As an example, I recently went out of town for a week, and boosted my FC to around 15 before I left. Just yesterday, two weeks later, it was finally back down to 3ppm (which is the minimum for my CYA level) and I needed to add more bleach. Compare this to daily additions during the summer.
You may consider turning down the chlorinator and, as Kim suggested, reducing your run time to 3 hours and see how that affects FC.
All that said, let's circle back to your 120 CYA. This is way too high (by about double) and your chlorinator is digging you a deeper hole every day. It's time to consider getting rid of the chlorine pucks completely, turning off that inline chlorinator, and converting to bleach. This will save you having to drain even more water than you already need to (right now, you need to drain about half the water in the pool to get CYA down to 60, which is a manageable level for sunny Louisiana). I inherited my pool with a new-to-me house last April and had a CYA in excess of 300. I had to drain nearly the entire pool to fix that, and with a vinyl liner, a full drain in one go is NOT an option for you - you'll damage the liner and possibly float the pool shell. Every day you wait to stop using those pucks is even more water you'll waste having to drain a few feet, fill a few feet, drain a few feet, fill a few feet - over and over to get that CYA under control.
Do yourself a favor right now and switch to bleach to stop the CYA from creeping higher and higher.
