Yes. As per above, they will (and must) behave as a single inverter. Both inverters expect the other to be there behaving identically to itself. If one inverter hits low DC shutdown, the other inverter will shutdown as well. If you simply unplug the VE.Bus cable between them, they will both shutdown. Hopefully, that addresses all of your following questions.
You can still keep the same setup you have, i.e., AC2 out can be configured to shutoff. Additionally, if you have a GX and a BMV/Smartshunt, I'm 99.9% certain you can program the criteria based on SoC. I've personally used assistants to trigger and terminate AC charging from grid based on SoC and the general flag. Should be able to do the same with AC out 2. The benefit of using SoC means you don't have to deal with voltage drop due to loads, which can trigger above the intended SoC.
If you did split phase, you could use the L2 inverter AC out 2 only - without connecting AC out 1, thus you would get the desired behavior, i.e, L1 inverter AC out 1 to L1 leg on panel, L2 inverter AC out 2 to L2 leg on panel. L2 leg shuts off based on your current criteria. If you wanted the L2 inverter to still power some loads, you could setup a separate panel.