The large battery pack lists a "normal/standard charge rate" of 5A. Assuming your charging at that rate, six of them needs somewhere in the vicinity of 1000W, probably a bit more to allow for power supply conversion inefficiency. Assuming the power factor of the 48V power supply isn't too bad, you ought to be able to reasonably charge six at a time with a 2000W (nominally rated) generator, or so it seems to me.
My impression is that the Champion generators have a bit better reputation than the others on your list, but that's just an impression, not backed up by any real data. I wouldn't be surprised if some of the others are actually identical except for the color of the plastic and the sticker on the side. I'd probably look at either of the 2800 W champions if I were in your shoes.