I used a BatteryMINDer to desulfate the big AGM's in hour stick house solar battery bank. It really helped both issues you describe. My bank is four 12 volters in series, so I used the 8 amp 12 volt charger, doing one battery at a time. One battery actually took a week before the Minder said it was ok, and not overly sulfated.
BUT
I have two seperate banks, which can be individually selected. I did the above on the bank which was out of service. I don't know if the desulfation would hurt my Xantrx inverter, and did not want to find out the hard way.