Hope this might be useful from an amateur... CYA might drop very slowly. After my last year's 2/3 draining and getting it down to 50, it's now about 40, probably mostly from backwashing and winterizing. However, using just hypochlorite all the time (12.5%, aka liquid shock), the CYA (measured by Taylor kit) continued to drop very slowly. I now sorta alternate liquid and occasional dichlor powder, the latter to maintain the CYA in the 40 ppm range. I simply switch the filter valve to Recirc to add them thru the skimmer and then switch back to Filter; then stir it up for 2-3 hours/day. Works well.
TFP does not recommend added any chemical directly through the skimmer to avoid potential damage to the equipment.
(But make sure--as I learnt--to add stuff and stir either in early morning or evening to reduce loss from sunlight breakdown.) In my 16x32 IG pool, I use about 1 qt 12.5% liquid or 1/3 lb of dichlor per day. And it' sparkling clean, free chlorine (at midday) 2-3 ppm.
If your CYA is maintained at 40ppm, to be sure of keep algae away, you need to keep the FC ABOVE 3ppm at all times and not let it drop below that by the next time you add chlorine.
Note too that I keep my pH fairly low, around 7.2 (chlorine effectiveness goes down drastically with higher pH, > 7.4).
This is not true when there is CYA in the water. With CYA present, the chlorine effectiveness degradation is greatly reduced to the point where it is nothing to worry about when the pH in the in normal pool ranges.
Note also that although liquid hypochlorite is extremely alkaline out of the bottle, it ends up neutral when it breaks down and releases its chlorine, and doesn't raise the pool pH.