The new Starcrafts have a decent converter/charger as standard equipment. I would plug the Shore power cord directly into the Honda with an adapter. Use a simple battery tester (spacific gravity) to monitor charge until you learn just how long it takes with your unit.
Then and only then, if the preformance was not sufficient, I would either upgrade the converter to a PD9240 or get a 40A portable charger. Skip the 10A chargers, as the stock converter will do a better job.
Does your trailer have a converter on it: If so, that's your battery charger
If not consider a PD 9245 or 9260 converter. This runs the 12 volt systems on shore power and is about the largest the kilowatt Honda will power
A kilowatt Genrac will run a 9280, however 1: It is a "traditional generator" and 2: the unit routinely delivered more than it's kilowatt rating without complaint
(I know for a fact I pulled 1200 watts off it more than once)
Nothin adds excitment like something that is none of your business John is Near Kenwood TS-2000 housed in a 2005 Damon Intruder 377