Pucks will not add chlorine as fast as you need it. I would recommend only using liquid chlorine (bleach, liquid pool shock) for your sanitizer except when going on vacation. Pucks will just raise your CYA even higher. The results of that will be that it will be even harder to maintain chlorine in your pool.
Go get bleach or liquid chlorine (either from WalMart or Menard's/Home Depot, etc). Add about a half gallon a day. Report your results and let's go from there.
Trace amounts of algae are too much. I recommend getting a better test kit (Taylor K-2006C). Worth every penny and I promise it will pay for itself over the season.
I have a relatively new vinyl liner and understand your concern. If you follow the forum's advise, your water will be sparkly clear and your liner will be just fine!
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