The charging situation is that dire. Lead-acid batteries, whether wet cell, need to be charged at about 1/10 capacity per hour for maximum life (number of charging cycles) and at most 1/5 capacity per hour to prevent damage. That's an average, the first 50% can go in at a higher rate, but topping them off takes progressively longer.
This is why solar works so well, even though the charging rate might be low as a few hundred watts can be the right rate for topping them off after a generator driven charger or an alternator feeds the high rate part of the charging cycle.
If you are going to run a generator, whether through a lame RV converter/charger or a dedicated separate charger, if rate is high enough it works really well for the first few hours of charge, 30-50% of capacity to about 80% of capacity, but charge rate works down towards a trickle from there, if the intention is to not damage the batteries.
This is where newer battery technologies like nickel metal-hydride and various lithium rechargable types (many still at development stage) have an advantage. They can be charged really, really fast on intermittent fast charge cycles, i.e. some of the technologies can be safely charged faster than they can be safely discharged. But with respect to expense, and commercial availability, this is a whole new area.
In your situation, I would be adding solar, to pick up the topping-off charges and carry the daytime computer loads, and to get through the night on the furnace, at least double the storage. I have two SRM-24 batteries, and when fully charged they struggle to run the furnace all night on a 20 F night.
