That looks like Gneiss (the rock). It is typically inert and not really effect your water... however depending on what it formed from that is not always the case.
You can't soften water by adding anything to it - it just doesn't work that way.
What is the KH of your well water? That can go a long ways to stabilizing your pH.. if your KH is low, adding the neutral regulator or otherwise increasing KH would help keep your pH more stable... but just letting your water sit and off-gas will also prevent any pH swings that could be occurring from any dissolved CO2... because it may be coming out of the tap at 7.6 because of dissolved CO2, which causes the pH to rise when it leaves the water... so you see it rising to 8.2.
Have you tried just letting it sit in a bucket for a day or two to see what happens to the pH without adding anything?