I'll be honest with you: I'm not quite sure what's going on at this point. Some further guesses: maybe your hair actually likes cones, but easily suffers build-up from them. If that's the case you can try going right back to cones w/the understanding that you will have to shampoo/chelate more.
... Or your first guess could be correct: a problem w/soft water. Two major chemical compounds in hard water are calcium carbonate and magnesium sulfate (epson salt). You could buy some distilled H20 and add epson salt, which can be purchased at the drug store and a lot of grocery stores. You may have to research or experiment w/how much to add. See if using that for a few washes turns your hair around. If it does, you may have located the culprit. Outside of that ...
Other considerations: Have you been under unusual stress lately? Are you experiencing any health problems or have you changed your diet? Are you peri-menopausal or menopausal?