As they said and a key point being 13.6 vs 14.4 volt converter. If yours only goes to 13.6 volts you may want to upgrade. It's an important part of cutting down on generator run time. Don't go by your monitor panel for battery condition, get a digital volt meter and basically stay above 12 volts. Using a digital volt meter do some checks at your converter vs at the battery bank to check for substantial voltage drops which increase charge times. Sometimes it helps to increase the wire size.
If you start doing regular discharges to 12 volts or so day after day you may need to watch you specific gravity or at least understand what is going on there so you are truly getting a full charge. As far as using an inverter and battery bank sizing read up on the Peukert effect and keep the battery cables short and big.