Hi,
You have two choices for getting batteries truly full. One is to use shore power and the other is to use solar. No one in their right mind tries to get to 100% state of charge running a generator.
You ave over thinking this whole issue. Calculate how much solar you need, go buy a quality charge controller and the necessary number of watts of panel. Use pwm or mppt. If the system is sized properly to the type of controller chosen it will be a successful installation.
If the inverter shuts down at 15 then 14.9 should be the max charge voltage under all circumstances.
Trojan wants batteries to be exposed to 15.8 volts. It would behoove you to have dual banks so that one can be charged while the other is in use, with easily adjusted charge maximums and appropriate disconnect switches.