What timeframe are you seeing? After a regen, water is fine for the first 20 gallons, and then gets salty for the next 200 gallons, or what? Or after a regen, water is fine for the first day, and then gets salty for the next 6 days, or what?
If the problem was that the water was salty just after a regen, and then cleared up, there would be an easy solution.
I suggest that after a regen, note the brine level. Then when the water has become salty, what has happened to that level?
To note the brine level, you may want to insert a yardstick or dowel down the brine tube as a dipstick.