If your water is soft then there must be some other base in your water to make the alkaline pH result (not the usual KH/pH relationship). Therefore my understanding is usual additives to lower pH by making water softer will not be as effective as that isn't the cause for pH reading.
I think that leaves you with a couple of fairly easy to do options;
a. Get some RO water from local shop? And experiment mixing it with your tap water to get the desired ph level before using it in wc to gradually lower your tanks pH.
b. Collect rain water to use for wc (this might even be slightly acidic).
Of course all this goes out the window if something base is actually in your tank causing the pH to rise after it enters the tank. What is the usual readings of your tap water (the low kH and gH might be due to depreciation in the tank too).
I have opposite water to you in that my KH is over 200ppm gH is over 500ppm and my tap water is 6.9pH.