A few quick notes from an installer here. (BTW we use a bit of Sol-Arks and 90% of our installs are off-grid.)
Last year we probably installed 40 or more Sol-Ark inverters, mostly off-grid.
I agree that they are not ideal for off-grid, much better suited for grid-tie and backup for critical loads. We still used a fair amount of them because of how integrated they are with their all-in-one design. But we have learned that we need to upsize them in comparison to what we would install in Schneider or other brands of transformer based inverters. (We would say a Schneider XWpro is more capable than a Sol-Ark 12K when it comes to grunt power.)
-ANY SOL-ARK SMALLER THAN THE 15K WILL STRUGGLE WITH 120V SURGE LOADS!!!! And I believe any high frequency (transformerless) inverter will! They don't have imbalance tolerance, and a transformer based inverter has much more oomph!
-A Schneider SW4048 would run what you have! (Although I would recommend a soft-start pump such as the Grundfos.)
-Transformer based 120/240 split phase inverters (such as Schneider SW and XWpro) generally are rated to handle a 70% imbalanced load.
-Sol-Arks are not configurable for 120v only output! They basically have 2 120v inverter circuits that have a controlled phase angle according to the setting you choose in the menu. (120/240, 120/208, etc.)
-A side note- when configured for 120/208 3 phase, one inverter will only provide 2 of the 3 legs, you need at least 2 inverters to get actual 3 phase output. (We have used single inverter 120/208v configuration in scenarios where there was existing 3 phase but the customer wanted to have some backed up loads- office equipment etc., and so the critical loads panel is 2 legs at 120/208v 180 degrees phase angle.)
-Note* even a Sol-Ark 12K WILL OVERLOAD at times if you have 120v surge loads such as motor starts!
-I personally have Victron inverters stacked to make my 120/240v (because of the endless "tinkering" possibilities with their venus OS), but if you want to have a bulletproof inverter that can handle imbalance and surges, go with a transformer based split phase inverter and a separate charge controller. (personal preference on charge controllers is Midnite Classic or Victron)
-In terms of off-grid and no internet monitoring- I'm not sure that you will find that in any name brand inverter out there. Everything is online anymore seemingly. I will say though, I love Victron when it comes to their GX devices. (I have a Cerbo GX.) Also, Victron has bluetooth on many of their devices, and updates can be pushed through bluetooth, over the internet, or via usb flash drive.
-A load balancing transformer would probably not help much in your scenario, as the high frequency transformerless inverters don't have much voltage sag at all, and voltage difference between the 2 legs is what allows the transformer to "shift" the imbalance across to the other leg.
One more note* the latest firmware on Schneider SW4048 inverters puts out 128/256ish volts, which is very high! The solution is a "hacked" firmware file update. (not really hacked, I guess.... just an older file "re-named" so that it can be loaded onto the newer version SW4048) Just something to keep in mind. Things work at that voltage, but it just feels very high...