My suggestion is to do it all now, as it will almost never be cheaper in the future - plus the benefits can be significant.
Duke does not provide 1:1 net metering, in fact it looks like 1/3 (2022 NEM rates were 6.631c/kWh - 2021 NEM rates were 1.986c/kWh). That means for every 20 kWh you use at night, you'll need to push back excess ~60kWh during the day. If your goal is bill zero, you will be hard pressed to do it by solar alone. With 17kW system, I'm guessing you'll average 100-120kWh on a full sun day. That equates to more than half going back to the grid to get net zero.
In addition, if your area loses power, even though you have solar, your production is shut down also - unless you have batteries. This shutdown is required by your power company to keep excess produced electricity from outputting to the grid and into the line workers. If you have batteries, your system can isolate and continue working, albeit if your batteries are at 100%, grid is down, your solar will shut down and run off batteries. The excess electricity needs somewhere to go, so it turns off solar until the batteries deplete to a certain level before switching solar back on.
One powerwall would be possibly enough to run your lights, TV, computer, refrigerator, maybe a window air conditioner. It will not run your water heater, central AC and other major appliances. This will mean a subpanel with backup loads and some rework of your main panel. Instead of putting a few thousand into this rework, might be better to get another battery or two and use your main panel as the backup load center. In the event of an extended outage, you still have the capability to shut down excessive loads as needed. But, if you went with a subpanel backup load center, you can't move a main panel circuit to your backup panel after the fact - at least not easily.
I'm in the same boat - 1:3 net metering in Florida (JEA). I went with a 20.4kw system + 4 PWs. My grid usage since PTO has been consistently in the negative overall, but even with 4 powerwalls I still have times where my batteries deplete on consecutive cloudy days. I went with as much as my roof could handle and I could comfortably afford, and presently sitting at about 123% solar offset. 10.5 months in, and I've calculated a $4,507 savings - beyond what my conservative estimates were. I'm 1.5 months ahead of schedule

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Let me add this - I'm in a house full of teenage kids, washer and dryer may as well be commercial and my wife decided that now we have 'free' power, the AC is set far lower than it used to be (after 25 years of marriage, I know which battles to fight and which battles I am guaranteed to lose - this is definitely the latter). Not to mention my hot water heater may as well have a 'stuck on' switch - but I went with a heat pump hybrid and solved that by putting it in heat pump only mode, dropped from 5kw to 500w, but it does run ~ twice as long. Still far less than elements only.
hth