Yeah, basically this. Your other points are really good too, but this one sums my thoughts up nicely.
Yeah, given that info, I'd go with a dedicated components. You can show up at the place, kick on the AC inverter and should be good to go.
With an all in one, my concern would be the idle consumption would kill the battery in the off season between visits. You'd show up on site and have a dead batt.
It's also worth pointing out that with discreet components you can repair, replace, upgrade components individually and not be forced to take the entire thing out for commission for a failure.