Our water is pretty hard around here. I used a mix of 50% tap water with 50% RO water at one time. (Now I use CO2 and the pH problem is solved!)
Our grocery store, Shop 'n Save, now Kuhn's, has an RO machine. Water costs 39 cents a gallon if you bring your own jugs. If you do this, like LWB said, mix it in gradually, maybe 10% of your tank volume at a time, and don't go over 50% RO water.
Your pH of 8.2 or more is higher than mine - like QTOFFER says, check to see that something in your tank isn't raising your pH. What kind of substrate do you have? When you let tap water sit out to do the pH and hardness checks, you could also put some substrate and water in another cup, and compare those results to the tap water only cup. They should be the same unless the substrate is altering your parameters.