You are correct that you do not need to raise the calcium hardness level for a vinyl pool. You are also right that you can use baking soda to raise the alk some, but I think you'll want more like 14 or 15 lbs. That should take your alk to around 100. This is not critical and I certainly wouldn't do it all at one time or you may cloud the pool. Do it gradually over several days with smaller doses. Add it slowly to the skimmer while the pump is running. Your pH is also a little low. I would advise adding some 20 Mule Team Borax (laundry aisle at Walmart) to bump it up somewhere around 7.4-7.6. I think I'd do half a box at a time added to the skimmer in the same manner as the baking soda. You can do one right after the other with no problems.
By any chance do you know your CYA reading?
Hope this helps and welcome to the Pool Forum!
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