I wouldn't worry so much about the high TA until your algae problem is resolved. And yes, the high TA makes it harder to maintain a lower pH, but if you can you can just keep adding acid to bring the pH down a bit though that is not your top priority. The higher pH does make the chlorine less effective, but not by as much as you might think (more on that below). A bigger concern is how high your CYA is. When you say it is 100, is it really 100 or is it more than 100 (most test kits only start measuring at 100 -- if the black dot disappears before you get to the 100 line, then you have CYA more than 100 and will have to dilute the CYA cloudy test sample with clear tap or distilled water and then double whatever you measure).

Does your chlorine level hold overnight or is it getting reduced a lot from night to next morning? If it gets reduced a lot, then the chlorine is killing the algae and you have to just stick with it -- at least a drop in chlorine levels overnight would show you are making progress even if it isn't visible yet. Keep brushing the sides of your pool, run the pump and filter 24/7 and scoop up any dead algae each day/night. Even though Ben's chart says 25 ppm of chlorine will do the trick, it may be that you will need even higher levels of chlorine, possibly 40 ppm or even higher, due to the high CYA level you have (even if higher levels of chlorine weren't necessary, it will make the process go faster). It might be easier and more economical for you to simply drain and refill substantial portions (half) of your pool water to get the CYA level down since that will make the 25 ppm chlorine level much more effective. This is more important than trying to get the pH level down.

The difference in chlorine effectiveness between a pH of 8.0 and a pH of 7.5 at your chlorine and CYA levels (assuming CYA 100 is correct) is only 12% so that's why I say that it is your absolute chlorine level that is much more important than trying to get your pH or TA down right now.

As for any worry that a chlorine level of 40 ppm might be dangerous somehow, this level of chlorine is equivalent to having only about 0.5 ppm of chlorine without any CYA so is not particularly high. This is why I suggest doing the drain and refill because if you get your CYA down to 50 then a chlorine level of even 25 ppm is equivalent to 0.75 ppm without CYA and 40 ppm would be equivalent to 3.2 ppm without CYA. So, getting the CYA level down really leverages the chlorine effectiveness when you ramp up to high levels of chlorine.

After you are through with getting rid of the algae, you should abandon your use of Tri-Chlor pucks (tablets) as your regular source for chlorine and switch to the BBB method or use the liquid chlorine if you found an economical source.

Good luck and hang in there. You will conquer your algae problem if you just stick with the high chlorine (keeping it high through the day and night as much as possible).

Richard