I considered getting a third Powerwall, but it just didn't seem worth it to me. A/C here is a convenience and a comfort but not a life-or-death necessity.
However, now that my old A/C died and I didn't want to be entirely without it, I'm having a true soft-start A/C system installed. This is costing me a lot more than a third Powerwall would have cost, but the differential between the cost of this new unit and a straight replacement of the old unit is far less than another Powerwall would have cost.
Followup: It took a month from the time my old A/C failed until the new A/C installation was finished (everything happens slowly in paradise), and the old thermostat didn't work so they had to come back and install a new one (the old one was a Nest "smart" thermostat, which I had no use for, so the new one is a "dumb" thermostat) but I am delighted with the result:
The new compressor is variable-speed and the thermostat tells it, not only "turn on" or "turn off" but tells it how high or low to go, so the hysteresis is almost completely eliminated. The indoor temperature remains much more constant, eliminating those long periods of waiting for it to turn on when it's a bit too warm, or waiting for it to shut off when it's a bit too chilly.
And I've confirmed on the Tesla app that when I turn it on it starts slowly, stepping up a few hundred watts at a time, so there's no sudden large current drain. I fully expect that when there's a power outage, my solar and/or Powerwalls alone will be able to start it.
My house cleaners were here today and after a month of open windows it took them twice as long as normal to clean my house, and that was cleaning only the main living area (the upstairs) and not cleaning the balcony or downstairs. So, twice as long to clean 2/3 of the house, because of all the dirt that blew in because I had to open the windows when the A/C wasn't working.
It probably would not have been worth replacing the whole A/C just to get the soft-start and variable-speed compressor, but the cost of replacement doesn't hurt nearly as much since it left me with an A/C that's so much better.
If you're installing AC and can afford it, I recommend a variable-speed compressor.
Note: I don't know if "variable speed" is the correct terminology, but for non-technical purposes it describes what this is.