BFL13, when enough amperage is presented, a depleted battery can jump to full regulated voltage -instantly-.
Amplification. Your batteries get depleted to the point where they are the most charge sensitive. Charge receptive.
Keep feeding them increasing amounts VOLTAGE LIMITED amperage until such time as voltage rises to the magic set point of 14.0 - 14.4
I regularly hammer my discharged 2-volt cells with 24 volt amperage approaching five hundred amperes and they respond by instantly going to 28.0 volts and staying there until they charge.
If generator run-time is not an issue, then this is a moot point. If you have connection to the Tennessee Valley Authority power grid this is a moot point. If you have a large generator laughing at a piddly charging system then this is not a moot point. Do the math and figure out how much money just in fuel one single battery charge costs you. Then factor in the kWh available by the batteries for that money. Surprise! Please don't have a stroke when you see the stupendous cost of each kWh. Oh forget about trips for fuel, wearing out the generator and insignificant stuff like that.
Having an MBA, it conflicts with my MEE. An engineer whose motive is to do the most with the least amount of money. I've run the numbers on this area so many times I see them in my sleep. I wish I could do this with solar. But the damned clouds keep getting in the way. Having a thousand dollars worth of food go bad in the freezer, or Jesús' four thousand in lobsters go bad is not an option. "The Store" is a seventy mile round trip.
When that Kubota starts, it is allowed to warm up for three minutes, then it grunts. No free rides. I don't have time, energy or money to play games battery charging. Diesel is almost (four dollars a gallon) down here too. The nearest gasolinera (Pemex Station) is a forty-mile round trip.
