I'm not sure of all the systems out there and have never had to shop for an inverter so I am surely not qualified to recommend a specific product or talk about the virtues of one over another.

I have followed other discussions on other bus sites and find there are inverters and then there are inverters. Ditto with generators. The key to our comfort is having generators and inverters which supply clean power that does not adversely affect all of the devices we tend to use.

With respect to the self start, I do not have a clue as to how to test your specific one. What we have is one called "Watchdog" and it can auto-start due to low battery voltage or loss of shore power depending on how we set the switches. It also shuts the generator down if there is a cooling problem or oil pressure problem.