Kabs996. I used to have the same issue as you for my first two years of pool ownership. I have a 18 ft round 4 ft deep, and I used to use trichlor tab pucks, and I couldn't figure out why I was getting algae outbreaks in the middle of July for 2 years. After coming to tfp and realizing that it was gradually raising my cya levels and that the chlorine was not enough to sanitize the water, it made sense why I was getting algae outbreaks at a certain time of year.
Furthermore I am on a cartridge filter myself, and for 4 years I couldn't figure out why I would get sediment in the same exact spots on the wrinkled part of my liner floor 20 minutes after vaccuming. Everyone here swore it was algae. When I touched it underwater it felt gritty but it dissipated quickly after touching. Came to find out four years later that my manual vacuum head was leaching very fine particles of sand and crushed seashell, which was used as fill weight after a plug came out of the head and dumped the crushed seashell and fine sand all over my floor. Surprisingly my skimmer sock and my 10 Micron Pleatco cartridge filter was not picking this up. I attempted to attach a 5 Micron bag to my return jet, got rid of the vaccum head, and the problem went away. It turns out that the sediment was sitting in my return jet hose and outlets from the ribs and the eyeball, and would gradually disburse in the same spot and the pool 20 minutes after vacuuming.
I also strongly recommend you do not use the trichlor pucks as it will raise the CYA. You want your CYA between 30-50 ppm if your pool is a non salt water generated pool. You definitely do not want to place any trichlor pucks in the skimmer basket as it will corrode your pool pump components.
Stick with the Bleach borax and baking soda or BBB method here at TFP, you won't be sorry you won't have any water chemistry problems and you will definitely save a lot of money. Bleach, Borax, Baking Soda and Muratic Acid is all you will need to maintain your water chemistry, that and maybe some conditioner or stabilizer or CYA if your water is below 30 ppm.
All bleach and pool chlorine is sodium hypochlorite, which adds no additional CYA to your water. Stay away from the trichlor pucks, di chlor granules, and calcium hypochlorite
"shock" packets, unless you specifically have a plaster pool and need a certain level of calcium hardness in your pool. Shocking a pool is a method not a product. Shocking a pool simply means elevating the chlorine levels to a certain height and level to sanitize any imbalances with your water chemistry. Shock is not necessarily a bunch of granulated chlorine that you throw in a pool, although the pool and chemical industry would have you think otherwise.
Once your water chemistry is properly balanced, including your CYA to Chlorine ratio, you probably won't need to add more than one gallon or 121 fl. oz. of bleach a week.
If you are having water chemistry issues, or algae issues, follow the SLAM process until the 3 criteria are met. Order the TF-100 test kit or the Taylor K-2006 C test kit. It will be the best investment towards your pool and in obtaining valuable information on your water chemistry, and adjusting it accordingly.
Pool School - Chlorine / CYA Chart
Before you go the DE route and spending money to change out for your cartridge filter, I would consider getting a 5 or 1 Micron bag to put over your return jet and see if that helps with better water clarity.
I may be considering just wrapping my cartridge filter with 1 Micron polyester felt material. Duda diesel makes the bag and the felt material.