You don't need a better converter, but you should always carry a portable charger as a back-up at least a 10a but 20a is better. Then even on shore power, if the converter dies, you can still run 12v on battery while 120v does the 120 stuff and runs your portable charger too if needed. This lets you get a new converter in slow time at a good price instead of in a panic at a high price.
One thing is if you will be on shore power your converter can do the 12v stuff so all you need a 12v battery for is to run the emergency breakaway set-up (it's the law with trailers) going down the road, so buying extra batteries now will be a waste starting next year. After that you will only need a single 12v battery.
So you have to do a bit of figuring how often you will do these off-grid weekends this year and how much battery that will require so you don't get too many batteries.
BTW, my mother used to sing that song while washing the dishes, so I gather you must be a heck of an engineer! :)