Usually a clarifier would only be needed or help if what is in the water is too small to get caught in the filter, such as a colloid. Algae usually clumps up, but some items like lanthanum phosphate precipitate when phosphate removers are used don't filter out well without a clarifier. Certainly given how long you've been shocking and filtering, it would be something to try as a last resort.
I'd say you've got three choices with regard to a clarifier or flocculant. You can use PolyQuat 60 which is both an algaecide and a weak clarifier. Though not as powerful, it will eventually break down so is a more "get in, fix the problem, get out" approach. The other choice is use of a powerful clarifier such as
GLB® Clear Blue® (I've used that in my pool when a vendor had me try out a phosphate remover that severely clouded the pool as an experiment -- it cleared the pool overnight). Another choice is to use a flocculant such as
OMNI Liquid Floc Plus, but you need to be able to vacuum-to-waste and I doubt you are able to do that with your cartridge filter since they usually don't have the multi-port valves that are used with sand filters for backwashing, waste, recirculate, etc.
You will need to clean your filter after use of the clarifier (after the water gets clear).
By the way, I'm assuming that you don't have a filter problem or a circulation problem and that you've been regularly brushing to get material to the filter. If you find that the cloudiness is only in areas of poor circulation, then I'd focus on that instead.