I would suspect the bleach is old. It loses strength over time. Very good chance Big Lots got a deal and it's just too weak for your purpose.
You are much better off finding a pool store that has liquid chlorine, if you can get a gallon of 10-12.5% for around $3.00 a gallon that is a very good price. Plus, because it is double the strength, that means less jugs to carry.
Otherwise Clorox brand, TArget/Walmart store Brand, and Aldi bleach are also good.
I would stay away from discounters like Big Lots and Dollar Stores.
Besides the problem with the bleach, you could still have an ammonia issue, which can cause huge chlorine demand... The fact that your CYA lowered on it's own since the winter, shows there may have been bacteria that entered the pool, consuming the CYA and turning it into ammonia.
What time of day are you adding the bleach? Try adding it after sunset, and let it do it's thing overnight without the sun destroying it. Even with CYA, you can still lose 50% of the chlorine to UV rays. Then test again in the morning and if its still very low, add more and bump it back up. The sooner your reach shock level, and
hold it there, the sooner this saga will end for you....
Hope this helps.