So 3,000 W is the spec I need to tell the installer that I want to add to my system? Or am I mis-translating? What is a "Wp"?
You will need to produce about 3000kWh per year beyond what you're currently producing, maybe a bit more given your anticipation of reduced production in 'normal' years, though our production has been pretty consistent for 3 years. In SoCal, depending on your roof orientation, you should be able to get at least 5 (hours per day) times your AC rating, as an annual production average. You didn't say whether the 5.9(?) kW rating on the system you have is the DC or AC rating (DC is higher,there are losses when converting to AC and then feeding back through your meter to the grid).
As an example we have a 3.44kW DC system, which rates down to about 2.98 AC. We produce about 5800kWh per year. That covers our house, about 8K miles per year on the Leaf, and a bit extra which we get poorly compensated for, but we're at our objective which is the same as yours, to actually net to zero usage, not just zero dollars.
The 3000kWh estimate is based on 13,000 miles / 3.2 miles per kWh (that's what we get from the wall) = 4000kWh minus the 1000 excess you have right now.
To make 3000kWh a year means about 8.2 per day, divided by 5 "nominal full sun hours" is 1.6kW AC, so you need about 1.85kW more in panel rating.
As to how you might add that sort of capacity to your existing system - various factors there. If you went with microinverters it should be pretty straightforward (you've probably got a 6K inverter right now, you can't just add panels to it, and a dedicated second inverter for just 1.85kW in panels may not be cost effective. )
You could go for a 2kW AC (2.3 or so DC - eg. string of 10 230 watt panels on a dedicated inverter or microinverters) and you'd probably be looking good.
We might end up in a similar position if we were to someday get a second EV.