Hi cornercarver, and welcome to the forum!
You are on the right track--the key to clearing the algae is going to be achieving shock level (12-15 ppm for a 0 CYA pool) and then maintaining it until the pool is clear and you don't lose more than 1 ppm of chlorine when measuring at night and again in the morning before the sun hits the pool (that way you're measuring actual chlorine use in the pool, and don't have to guess at how much was lost to sunlight). That being said, anytime you have high chlorine levels, you're also going to have falsely high pH readings. So...I would use the acid to lower the pH into the 7.0-7.8 range first, and THEN shock the pool.
Typically we would recommend that you leave the pump and filter running 24/7, backwashing the filter as your pressure gauge indicates, but can you tell me what size pump and filter you have? If the filter is over-driven by a pump that's too large, which sometimes happens in AG pools, the pump can actually push the algae through the filter and back into the pool, except in smaller pieces.
Regarding your test strips, I'm hoping you've realized that they're not very reliable, and that's why you're using the 6-way kit, which is actually a relabeled Taylor kit. You're right in that you can add stabilizer to the pool to raise your CYA, but I would get the pool cleared up first.
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