Hi Scpool....

Do you already have a chlorine feeder? Or are you planning to buy one? They can be used successfully with trichlor pucks (that's the ONLY kind of chlorine you put in a trichlor feeder!) but you have to keep a close eye on your pH and CYA levels. They actually work better as a supplement to bleach than they do as the sole chlorine source for a pool, especially one in your climate.

Adding CYA is not going to substantially lower your pH, whether you add it through sock or skimmer. What exactly are you adding when you say you added BBB and had to readjust?