Out of curiosity, is your AC unit circuit one that is actually powered when the generator runs? A lot of time, the circuits powered to run when the generator is on are limited due to the generator capacity and are only there to run some lights and the fridge and freezer. It takes a big gen-set to run an AC unit.
I have the Schneider/Electric XW 6848 Pro inverter. Good for surges to 13 kw. Continuous at 6.5 kw. Off LiFeP04 batteries, 42 kw.
So every load is on this system. I do automate and disconnect many other loads to manage running off-grid.
Also have 3 other hvac systems at 2-ton. None have a soft-start, nor do they need it. 2-ton starts fine off-grid. I just have to observe my system limits of 6.5 kw