Do they still have the ~10kW restriction (nominal) on the panels for grid-tied systems? (I'm guessing that's why your system is 10.6kW)
Personally, I think I'd want to get more panels than that, biggish battery, and an EV, and try and be as close to off-grid as possible. But our house in Bangkok was built in the 90s, so I don't think the insulation in the walls is particularly great, all the windows are single-glazed, and some of our aircons are ancient.
Size of the battery would obviously depend on the choice of EV as some do vehicle to load, and some don't.