Can't raise chlorine

I'm newer to this site and have gained so much useful knowledge I didn't know since getting my pool four years ago. However, I can't solve my problem still. I can not get my free chlorine levels to rise. This has been a problem all season and three weeks ago I had a horrible algae bloom when comin home from vacation. I have since returned the pool to crystal clear and as of yesterday my test results (which were backed up with a test at local pool place for added accuracy) are:
FC 0
TAC 0
calcium hardness 220
CYA 40
Total Alkalinity 110
pH 7.6
copper/iron/phosphates are all 0

Local pool place suggests powder shock and chlorine tablets and that has lead to two seasons straight of fighting algae and cloudiness on and off (mostly on). After recent algae bloom I joined this site and learned more about chlorine. I bought four gallons of 10% liquid chlorine at Walmart and dumped in one gallon first night and next morning water was clearest it's been in two years but registered 0 chlorine. I did another gallon that night, followed by 1/2 gallon on nights 3 though 6. I still have three tabs in the floating diffuser as well. This all still leaves me with 0 chlorine within hours of adding. If my CYA is 40 what else can I do. I haven't had 10 days of crystal clear water so I will keep adding liquid if needed. The pool is in direct sunlight from 6:00am until 6:00pm so water is currently 84 and is used 3-4 hours a day by my 5 year old sun with my wife and I watching from deck or floating around. I have explained all this in length to pool supply store and they have no answers or suggestions. Thanks for any advice!
 
I am experiencing the same issue with my swg pool even after SLAM in which I may not have gone above FC31 using 4 gal of 10%.
FC 0
TA 100
Ph 7.5
CYA 70
CH 80

Just tested my SWG by trapping the water from a return using a syringe and FC was 2.5 at Super Chlorinating setting. Not sure this is the "norm" Keep us updated!


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