In an automobile, in addition to the isolator for the second battery (which is a great route to go!), you can also add a farad capacitor. A lot of stereo enthusiasts utilize them to stabilize power to amplifiers when the draw spikes. A decent capacitor can be found on Amazon for $100 and will assist with peak and start-up load through the inverter. Good luck, you’re on the right track! Always be prepared.
What, they don't junk X-Ray machines anymore? I think that's where my last 2 large caps came from. ;)
/johnny