My take: Connect both batteries together in parallel, having a master disconnect switch that interrupts the batteries from any 12V except for the break-away system.
If you have solar, connect it and leave it connected for storage considerations. Replacing the converter would obviate the use of a trickle charger as the newer converters will have the same function. The converter will also offer the capability of charging the batteries in a shorter time, something that is very important to those with generators. About the only thing "wicked" with the Genius charger is that the "boost" function operates at 16V (how many amps is unknown). That would be helpful to equalize an untended battery.
The OP doesn't state what's wrong with the original WFCO converter but I wouldn't replace it with the same as there are many testimonials as to the superiority of the PD converters.
It sounds like the SOC of the battery has been a guess (battery is dead on occasion). This is a bad situation as even a hybrid marine battery will eventually have an early death from discharging it to less than 12V, especially if no immediate manner of charging is present. A battery monitor, an inexpensive 12V panel mount gauge, or a hand-held meter will indicate the state of charge so that early battery death is not imminent.
