I think that you need to get the wiring diagrams from winnebagoind.com and check out the way your rig is supposed to be wired. In the owners manual it states that the engine should be running when deploying or retracting the slides. The engine charges the chassis battery and the house batteries simultaneously, no B.I.R.D. involved. Different than the Bounder we had.
The chassis alternator puts out more amps than the charger so running the engine will provide more power than shore power or gen set.
Which would put less strain on the batteries?