Using filtered water

[mcdonald_ajr]

I have very hard water (East Kent). Just did a Salifert KH/Alkalinity test which read 15.3 dKH which I believe equates to an alkalinity of 272 ppm.
I have a water filter plumbed in to a 3-way Franke tap, and when I measure the alkalinity of the water through the dual filter it shows 1.2 dKH which is 21 ppm. This filter removes water hardness, but I assume it can only remove the temporary hardness (calcium bicarbonate) and must leave the permanent hardness (calcium sulphate). I know it removes the temporary hardness as I use this water in my kettle, and get no limescale build-up!

I would like to use this filtered water for brewing, as it tastes very pure. My question is: What water treatment should I use?
My mashes are still too alkaline (ph 5.6 with 20g gypsum in 40 litres), and using the boiling treatment won't help, as the temporary hardness has already been removed.

Thanks, Anthony