We have the same problem ( hard well water, with soluble iron) and installed a softener that solves our problem. It's really not rocket science to install one and skip all the sales BS and enormous markup. Get one that has separate brine well and mineral tank and do some research on a quality timer valve ( Fleck or Osmonics- we have the latter but Fleck is better). You should be able to pull this off for $500-$1000 DIY and a day's worth of clean fun. As noted, you don't want that brine going into your septic tank unless you want another messy problem. Then it's best to supply your drinking water needs from RO (see if your cat will share). You will need a simple filter upline ahead of the softener to keep the chunks out of the mechanism.

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