The existing 6300 to battery wiring is good enough to run the 12v systems from the battery. So when you run the systems from the converter across the battery, that same wire is still good enough to run the 12v systems from the converter.
Battery charging is only from the converter to the battery on the wires joining them (on the other side of the battery from the wires to the system) They need to have the ampacity to get your 75 amps to the battery bank.
Inverter wiring is also high ampacity to run a microwave or whatever, so short fat wire to the battery is needed. This means the high amp charger and the inverter can share the same wires to the battery (as with an inverter/charger) Just mount the inverter and the charger near each other and run short fat wires from one to the other's DC terminals and from there onwards have one set to the battery.
The neg and pos paths don't need to be equal. It is a circuit, so you add the resistance of each part of the circuit. It is the total R that counts. Often the RV frame is a big part of the neg path and the frame has fairly low R, so all you need is a good pos path to get total R low enough.
There are many factors with inverters to consider, but that is another story. You can run a microwave with a MSW inverter IF the inverter is rated for running "motors" (inductive loads) You only need PSW for a few things like electric blankets and certain battery charged power tools.
If you have a few of those things, often they can be run with a small watt inverter. So folks get say a 300W PSW inverter for that and a big MSW to run the big things which don't need PSW (MW, kettle, toaster, hairdryer, etc) this saves money where a big PSW inverter costs so much compared with a MSW one.
"Sine wave" often means the same thing as "PSW" or "True SW" as opposed to MSW depending on Brand, but you can check the specs for how close the wave form is to pure (by having more little steps)
I don't follow why you think having a PSW vs MSW inverter has anything to do with battery charging. The inverter has nothing to do with it. You might be thinking of inverter generators, which supply cleaner 120v to a battery charger so it runs better than with some ordinary generators.
