Great stuff! That's exactly what I'm looking at lol. I had the 2 capacitor setup. I do not have a digital display like yours. Just a few switches that change from on, auto for fan control, temp control and a setting for cool, off and heat.
I got the soft start done correctly and everything is working smoothly now. I now am drawing between 13.5-16amps on the tests I did with a voltage drop only down to 114v. The surge is much lighter now. Even tested it while running the microwave and it still started up.
The other plus on the soft starter is that the micro air that you recommended has a built in 3 minute cycle period so it cannot short cycle my AC anymore either. If I try it just gets an error and then clears after 3 minutes and starts up again (was trying to force a short cycle but doesn't work so the 16amp draw was all I was able to get now).
Note that this was without the battery installed still but because the surge is less, there's still a possibility that the battery being hooked up would help keep the control unit functioning since it would have a good 12v connection. When the surge hits I wouldn't be surprised if it dropped down to under 10v on the DC side.
Unfortunately I already had things apart before testing the battery theory but now that my voltage drops aren't crazy that isn't something I can test without hooking all the old start components back up lol.
Thank you for the recommendation on the soft starter! Worked great and in the end it seems to of solved all of my issues.