Thank you for all the comments and suggestions. First thing I shall do is determine the details of my converter... is it multi-stage or not... and then manufacturer's information.
Some mornings I wake up thicker in the head than other mornings. I hadn't even thought that full-timers stay plugged up constantly. The consensus appears to be that the AGM batteries won't get hurt being plugged in all winter. At the same time they won't lose much charge if disconnected. So I'll likely use my battery disconnect switches - which interrupt the positive side of both house and chassis batteries - and monitor the charge level. And if the battery output drops... I'll throw the switches and reconnect to shore power.
As always... thank you for wise and well thought out options and suggestions.
