I think you may be a little confused about how things are wired currently. The 120V and 12V systems are isolated from each other, except in that the converter is a 120V load and simultaneously a 12V supply/charger. The fact that the 120V breakers and 12V fuses are mounted side by side is immaterial to their isolation.
A modern converter, such as a PD 9200/4600 unit, is a hardwired multistage charger. The possible advantages over something sold as a battery charger (which may not apply in every case) are that it is known to play well when left connected to the battery but not to AC power (it won't run down the battery unnecessarily), and to behave when other power sources are also present, and being hardwired to stay connected. Some battery chargers may have more sophisticated charging algorithms/techniques or more modes or controls to play with.
I'd suggest upgrading the converter portion of your electrical center to one of them, and leaving the remaining 12V distribution more or less unchanged. It may be worthwhile to run heavier power and/or ground wires to the battery, depending on what's there already. You would also need to bridge the two sections of the 12V fuse panel (the "filtered" and "unfiltered" sections) so that the converter, the battery (through the disconnect switch), and the newly joined 12V bus are all in parallel. Adding solar shouldn't cause any great headaches here.
There's generally no problems with having a modern converter, the charge line from the alternator via an isolator of some sort, and a solar charger all connected to the battery. There's also no problem with having most modern converters connected to the 12V system but not the battery; they have much better filtered output than your old converter. Some combinations of solar chargers and converters might fool each other into changing charge modes at times when you'd prefer they not when working together, but I can't really say how much of a problem that tends to be in practice.
