I confirmed that using the genset to run the built in charger is a complete waste of time and gas. With the battery down to 12.1v (about 50%), the charger would only put 13.2-13.4v and 9-12 amps at the battery. It would take hours to charge that way.
Starting up the engine instead would yield 14.4v and 20a at the battery.
But I had brought a basic 40a automotive smart charger from the big box store. It would deliver 14.6-14.7v and 24 to 30-some amps. I could get a 90% charge in about an hour with it. 90% is when the battery is only accepting 6 or 7 amps. It takes a long time to put that final 10% in. So I got by on about 1 hour of charging a day.
The charger sometimes would work fine even with the built in converter charger also pushing a charge to the battery. But a couple of days, the big charger thought the battery was full. So I had to turn off the converter's breaker, which also turns off the outside outlet I was using to power the charger! So then I had to run an extension cord from inside the RV out to the charger. Jeez.
The problem with the stock setup is A) the converter charger, and B) the cables. The charger is a typical low voltage charger, basically a little better than a trickle charger. It can be replaced with a Progressive Dynamics charger. But the cables are still a problem. At least on mine, TL ran them all over the place under the chassis before finally getting to the battery.
I don't really have the space to haul the separate charger around. But I haven't figured out my next move. At a bare minimum, I am going to make it so I can turn off the converter without turning off the outdoor outlet. :)