i have been periodically following along. I would possibly look into theory with respect to chlorine use and pool sanitation.
check out this thread and chart:
EDIT: You will find a simplified and standardized version of this chart at Pool School, Chlorine / CYA Chart. Chlorine/CYA Chart by Chemgeek FC = Free Chlorine in parts-per-million (ppm) CYA = Cyanuric Acid in parts-per-million (ppm) CYA ........... Min FC3 ..... Target FC ...... Yel/Mstrd...
www.troublefreepool.com
You will not have any CYA because that is a pool specific aditive to protect chlorine from being "used" by UV radiation (CYA reduces chlorine effectiveness while protecting from UV so don't add either). So with 0 CYA, maintenance levels of chlorine are considered 2ppm but you can see how various shock levels (SLAM in TBF nomenclature) increase and maintain chlorine levels until desired results are achieved. If you go below the chart, SLAM for general algea growth is 5x the maintenance level and SLAM specifically for yellow mustard algea is 8x the maintenace level. This tells me that the chlorine levels need to be based on the type of growth and extent of problem. your problem looks bad (and don't know type of growth) - so I think you are on the right track considering chlorine levels of well in excess of 10ppm. I might even go as high as 50ppm and see what happens.
Also note that proper pool chemistry for chlorine effectiveness wants the pH in the 7.2 to 7.6 range. Definately not above 8 so not having the pH low enough is likely preventing it from killing everything.
You will very much want a digital pH meter and a titration kit for measinging chlorine at very high levels - the FAS/DPD kind of chlorine titration kit. Taylor makes one that is good - K-1515-C is the kit with bigger bottles assuming you will be doing lots of these in the near term. K-1515-A is the same kit with smaller bottles. These kits measure both free chlorine as well as combined chlorine (byproduct of killing stuff) so you know how well the chlorine is working. Test strips generally are terrible and I would highly recommend against their general use in all circumstances. But, more importantly for you, test strips will be competely useless for measuring chlorine in the high concentartions that you are considering. A sister site to the one linked above,
https://tftestkits.net/cart.html, sells the standalone chlorine test kits with reagents from Taylor. I have purchased and use their products for my pool and they are excellent. Taylor products are obviously available from other sources too.
for pH meters, I have this one
https://www.amazon.com/dp/B01ENFOIQE/ref=emc_b_5_t and it has worked flawlessly. I also ended up getting all 3 pH calibration solutions - I think the kit only has two levels (which might be fine for what you are doing).