HI, and welcome to the forum!!
Yyes, you are exactly on the right track!! So--how does your water look, and is the algae still present? If the algae is NOT still there, then you need to be keeping your chlorine between 5 and 10 ppm at all times, because your stabilizer is high at 70. If the algae is still there, then you need to bump your chlorine up to 20 ppm and hold it there, with pump running and brushing daily, until the algae is dead and the filter has a chance to clear it all out. I would remove your trichlor pucks from the floater, though, because your CYA is already high and is going to continue to rise as long as you're using them.
Your alkalinity actually is ok at 90, but in a vinyl pool will be okay at 130. Don't raise it any more, though.
And you're right not to put calcium in your pool. It is necessary for plaster/concrete pools to keep the water from leaching the calcium from the concrete, making it brittle--but in a vinyl pool there is no calcium to leach, so no need to add more calcium if there's any at all already in the pool.
And just one other quick comment--I would always, always trust my own drop-based testing over that of the pool store's. If you want them to test it to verify your readings, fine--but if they differ, I would always go with your own....
Janet
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