My setup is exactly as you have asked. AGM for Start duty and FLA for House. The charger is connected to the house bank only. The Alternator
is connected to a charge splitter, so normal "after start" charging
is taken care of by the Alt. Then for long periods, like Winter, I have a solar
panel and charge controller that is connected to the start bank only. This keeps tickling them over the winter months. But these AGM's will happily go for a year with little decrease in current, so I don't really have to have the Solar panels
. They were there, so I made good use of them.