'Super Start' does not invoke confidence of being a deep cycle house battery.
Or was the prior owner killing the chassis start batteries?
Either way that inverter/charger will easily take good care of the batteries when plugged in. Although you need to check if the chassis battery is getting maintained while plugged in. Many do not. Plugged in 24 hours all your batteries should be 13.2 to 13.5 volts on the terminals. You can add a combiner if the float charge is not getting to the chassis start battery.
The 12 Volt Side of Life