I just found your thread and looked over the data.
Your main panel is very similar to what I have. I am in Santa Clarita, still Los Angeles County, but I am on So Cal Edison for my electric utility power.
I have a Schneider hybrid inverter between my main panel and a small critical loads panel. Without the external CT's, exported power is totally hit or miss going back to the main panel. I ran without CT's in my main panel for over a year, and I just set a fixed current for the back fed to the main panel. That was far from ideal. It looks like the Sol-Ark in your case is only using battery power to run the loads in the backup/critical loads panel. And the exported power reported by the Sol-Ark is the energy going back to the main panel, but only some of it goes to the grid. The rest of it is powering all of the circuits that are still in the main panel. So when the Sol-Ark reports that it exported 40.2 KWHs on April 15th, your main panel may have used 30 KWHs of it, and only 10.2 KWHs were actually exported. But without the CT's you just don't know. If you log into your account on LADWP, can you get hourly energy readings for a single day? I can do that with So Cal Edison. And I was using that data to dial in how much I was exporting before I added the CT's to control it. If nothing else, hopefully, you can find the data for each day to compare with the Sol-Ark data.
$392.07 for a month of electricity beyond your solar production does seem high, but then I noticed it was for 57 days, so almost 2 months. Still a bit more than I would expect, but not as crazy. On April 15th, the Sol-Ark reported you produce 62.3 KWHs of energy from the solar panels. That is a lot of energy. My system on that same day did pretty good at 29 KWHs. I only have 4,800 watts of solar panels, so that works out to my system getting just over 6 sun hours. Do you have over 10 KW of solar panels? Looking at the diagram, you have 28 panels? That could easily be over 10 KW. My panels are 4 year old 300 watt panels, and I only have 16 of them. The odd thing is. my system made over 25 KWHs every day in April except for 4 cloudy days. I would not expect the weather to be that much different if you are still in Los Angeles County. But what I am seeing is the Sol-Ark may be letting your main panel use grid power while it charged the battery on extra solar beyond what the critical loads panel needed. That is a big reason why you need the CT's. It may have even been curtailing off PV Solar power when the battery is full, and it is supporting all the loads in the backup panel.
Do you have the same April-May billing from LADWP for the last year before you had the solar installed? If your energy usage was about the same, I would guess the electric portion of the bill might have been just over $1,000 as the Sol-Ark and solar panels produced about 2/3 of your energy needs. By any chance are you charging an electric car? or 2 of them? I am seeing a lot of double pole 240 volt breakers in your main panel. What all is in that main panel, you have a lot of circuits?
Yes, you really need to add the CT's to get the Sol-Ark to know what your demand is back in the main panel. Where is your actual main breaker? It that the big 4 pole at the bottom? Could the CT's fit on the cables or bars going into that?
It appears you have over double the PV panel power I have. So your system should produce about 16 Megawatt hours a year. April and May are my highest production months, but that will vary with your panel angles. You certainly use a lot more electricity than I do.