From a purely technical (can it be done?) prospective you can back up the whole house by connecting the Load side of the Sol-Ark to your main panel and then rerouting the main feeders to the Sol-Ark Input. From an Electrical Code compliance prospective its probably doable but perhaps difficult.
For example, I have done exactly what you are suggesting using a Conext XW+ 6848 but without involving the local building dept. I also live in So Cal. My installation is completely safe and grounded properly, just not sure what the inspector would think of it?
Briefly here is how it was accomplished. The original 100A meter/breaker panel was so packed full of S*&? after 2 room additions (before we purchased the house) and the installation of a grid-tie solar system, I wanted to upgrade to a 42 position 200A main but didn't want to go through the whole charade with the Bld Dept and SCE. Since the existing 100A service is on the outside wall of the garage, I installed the new panel, no meter, inside the garage behind the existing panel and installed a 2" nipple between the 2 panels. The existing 100A panel was completely gutted and retrofitted with the bus bar and interlocked breakers from a Reliance 10060 manual transfer switch. The 60A transfer breaker feeds the Schneider 6848 inverter input and the inverter output feeds the new 200A main panel through a 60A, 2 pole breaker. The 100A transfer breaker feeds directly into the new 200A panel via the main breaker that sits on top of the bus bars. So basically the transfer switch is acting like a maintenance bypass where the 100A transfer breaker is OFF while the 60A transfer breaker is ON so all power in and out goes through the Schneider inverter. However, if the Inverter fails it can be isolated from the system by turning off both 60A 2 pole breakers and power can be fed directly to the main panel via the 100A transfer breaker. Since the existing SCE UG wiring is rated for only 100A, the breaker is sized properly even though it feeds to a 200A.
You could do something similar by installing a manual transfer switch next to your main panel and doing exactly what I did without having to move any breakers over to a critical loads panel.