What kind of batteries do you have?
What is the total amp hour capaicty? Or battery size and number of batteries?
Are you limited by something like being plugged into a 15 amp shore power? Or are you somewhat unlimited by being plugged into 30 or 50 amp service.
You do have the ability to set the inverter/charger to a shore power less than what you actually are at, so say you are visiting a friend, you plug into their garage, and want to limit charge rate so input amperage is less than 10 amps at all times. You can do that, and the charger will reduce it's charge rate if the incoming amperage is not exceeding 10 amps.
13.4 volts is a little to high for a "Float" voltage. I prefer 13.2 volts. 12.5 is way to low of a float voltage, while 12.9 is just barely high enough to keep the battery from sulfating.
At some times, my voltage will reach as high as 13.9 volts, while in the absorption stage, it will go that high to quickly fill the battery while on a generator.
Fred.