From everything I have researched Carbon filtering then distilling is the purest water one can get currently. Its no doubt going to be acidic and can drop even to 4.0, the same as reverse osmosis, or when one adds pure l-ascorbic acid or lemon juice to water.
It's not recommended to drink 'pure water' by many water experts without first alkalising it as it will pull lots of minerals from your body, hence known as leeching.
Try using terramin clay and/or a pinch of himalayan pink salt per 2 litres. It will bring it back up another 2 on the scale.
Or just go with the basic carbon block filter or gac filter, as this is essential for every single water filter available to buy anyway.