Or... put an off switch on the refrigerator feed.
Yep - also a really good idea (in fact, doesn't even have to be part of the charging regimen. Just seems like a solid design to have a physical cutoff, especially for electronics that have to pay attention to soft switches).
Since any given solution doesn't work for all campers, my biggest thought was really about minimizing electrical draw/usage. Why energize the entire camper (and the converter and the onboard charger, and everything that comes on with shore power, etc), when just trickling straight into the batteries with a proper charger designed specifically for that kind of service duty seems to be the right intersection between need and utility.
I'm jealous of your storage setup, with "right next door" access. Ours is in dedicated, enclosed storage with power just shy of an hour away. Something about leaving the trailer with juice in it for months on end, without immediate supervision, seems like a problem waiting to happen (or even tempting fate). Good to know that it CAN do it, if we NEEDED to do it that way.
Right now, our camping is fairly curtailed - while we're weekend warriors at best (till the retirement comes), last year and this have been dedicated to some family-focussed issues that we're working through. Light is at the end of the tunnel, however, so we'll be back out there soon.
This place *waves hands around* helps. If we can't be out camping and enjoying our trailer, we sure can be talking about it!
Just my .02. Happy camping!