Since you are apparently using test strips since they can only measure Total Hardness and not Calcium Hardness (CH), it's hard to know if your number are correct. You can use The Pool Calculator
to calculate the saturation index which is around 0.3-0.4 so on the high side that could account for the cloudiness.
If your Cyanuric Acid (CYA) level is truly zero, then if your pool is exposed to direct sunlight it will lose half of its FC level every half hour or so. Either that number is wrong or your pool gets low in FC during the day letting algae grow which can make the water cloudy (initially).
I strongly suggest you get yourself a good test kit -- either the Taylor K-2006 you can get at a good online price here
or the TF100 from tftestkits.net here
with the latter kit having 36% more volume of reagents so is less expensive per test.
Try lowering the pH and see if it clears the water at all. If it does, then the water is probably over-saturated with calcium carbonate and you'll need to either do a partial drain/refill to lower the CH level or will need to lower the TA by following the procedure described here
. If, instead, you have algae, then you can get rid of it by following what is described here