I'm going to single step the project
First get a MPPT controller to see difference
Depends on your climate and panel to battery voltage.
If overcast skies and low light are a regularity MPPT kicks bottom.
If it's usually sunny then PWM with a panel Voc ~3V above absorption can hold it's own.
Cable costs and the ability to oversize and hybridise my controllers has me phasing out all my PWMs
Second re-mount my panels to get more from them
Possibly rewire them into series sets
Earlier start up and later shut down with series strings. If you go too far the controllers start singing something woeful.
Third, Get a new inverter
Modified sine wave does not have a true neutral.
Pops the inverter when neutral touches ground (ask me how I know)
That's the high-frequency topography not the sine resolution. If it's transformerless and or centre tapped earth then smoke will escape.
Rewire the batteries into 24 or 48 volt config
24v is very handy because truck appliances and switchgear control convenience.
If your needs will never, ever, ever exceed 4kVA then it's ok.
If they conceivably will, make the move early because the later you do it or pursue a too low voltage the more expensive the legacy gets.
Add charge controller, and/or replace the existing panels.
More is more. unless you use them to leverage more hardware/need the real estate yer probably better off keeping them and throwing them into the mix...on a separate controller.
I figure all of the above steps are isolated enough that I won't wreck the existing system while working on it.
The amount of gear I've blown working on live circuits...

48 volt charger?
Feed an MPPT solar controller a PSU and current limit the charge controller to 80% of the PSU output.
You can use a transfer switch/relay between a solar array.
battery balancer ?
No need unless the battery is made of orphans of mixed providence.
more fuses between batteries?
One per string and cable size reduction.
I'm still learning
Me six.