Installing a converter is a piece of cake. Since you don't understand the AC so much, leave it to someone experienced.
The DC is where you could be focusing your attention and the new converter is a good first step.
I'm just going to say this as straight out as possible: Some of your DC wiring needs to upgraded to a larger wire size. For your projected use, the size of storage batteries, and presumed charging needs, the wire connected from inverter to batteries, batteries to converter, and from solar controller to batteries needs to be large. I would aim for at least 4 AWG but I don't know any distances involved. All of these wires should be fused. You don't need a fuse between modules and controller but a manual circuit breaker is handy in case you want to work on the system without disconnecting wires.
Battery isolator: Something similar to
this.
