Your cloudiness is most likely dead algae carcasses, indicating the SLAM, along with the fact you had zero FC for a period of time.
If trying to clear it, keep the pump running 24/7 and brush to keep the dust suspended and headed to the filter.
I tried several clarifiers for plaster dust. Most didn't work for me, but one that did was called poly-diallyldimethylammonium chloride. The natural eco polychite types did nothing for my plaster dust. If trying either, stick to the recommended dose. More is not better; it can be worse. Some people have success with it filtering algae carcasses. No one here that I've noticed recommends regular use, so don't buy more than one jug in any event.
It's entirely your call of course. But here's the recipe if you refill. I have little sense of USA prices, so someone else can correct me easily enough.
4 lbs CYA (aka stabilizer, aka cyanuric acid) to achieve 50 ppm CYA so the chlorine won't burn off - Home Depot, Lowes, Walmart, pool $tore - around $15
2 gallons 8.25 bleach (plain, unscented, not splashless) to hit 16 ppm FC (shock level) to kill off whatever is hiding on the walls, etc.
9 gallons to cover 30 days at 2.5 ppm FC loss per day
11 gallons total - $2.50 per gallon - call it $30
Needs test numbers on fill water to refine this, but...
Guess TA is 50, raise it to 70 - 3 lbs baking soda $??? - say $10? I have no idea
Guess pH is 8.2 - lower it to 7.6 - 20 ounces of 15% muriatic acid (MA) or 10 ounces of 31% - buy a gallon and will last a long time - $??? - say $10
Ready for swimming at this point, when water is warm enough and clear. Optional: Buying a cover will heat it faster and keep it warmer, maybe $70 to $100.
Fill water at $10 per thousand gallons - $100
Total $165, pretty much a sure thing ready for family visit
If you SLAM:
Drain/refill half assuming CYA is high $50
Total guess 15 gallons for SLAM - that's around $40
9 gals bleach for next 30 days $23
Other stuff to have on hand for maintenance - $20
Total $133
You would also need a pool brush and pole, leaf scoop, vacuum, but sounds like you have that gear. Maybe some small scrub brushes, have all the family jump in the day after you fill it (brrr, hope it's hot out) and scrub it around any algae hidey places. An old toothbrush for hard to reach places.