A soft starter will nearly be a must, as even my rinky-dink A/C used to draw more than 90 Amps during start (with the soft-start, it draws about 24 or so). You'd be close to the current limit, even with two PowerWalls. Tesla will install the soft starter for you, included with everything else.
With two PowerWalls, you'd have 27 kWh maximum (if they're both fully charged when you start running your A/C in the evening). My 3-ton A/C draws 2.6 kW when it runs, and my house takes about 0.3 kW to keep things running at night, so, 2.9 kWh for an hour. So if I ran it for 9.5 hours continuously, I'd completely drain both fully-charged Powerwalls.
However, of course, the A/C does not stay on continuously. And, I've set up my Nest to keep things comfortable during the night-- start out at a higher temperature, but drop the temp every couple of hours. That way the A/C runs more efficiently as the ambient temp cools down further at night. So, it doesn't have to run as long each cycle, but it keeps the rooms at a nice temperature. So, let's say I run the A/C a total of about 6 hours at night (4 cycles, 1.5 hours each cycle). That would put total power consumed at 17.4 kWh. You can use that as a point of reference. It'll depend on how drained your PowerWalls are when the panels are no longer producing, how much other power your house draws during the night, and how many total hours you run the A/C at night.
From early March to the second week of July, I was 100% running on only solar and one PowerWall, so I'm rooting for you. I imagine I'll return to that in Fall, and most of Winter.
Best Wishes!
