The 60 amp converter will be too much for the 1000w gen, but the 1800 could handle it.
It would be interesting to know just what the SOC on two 6v AGMs would be when the charger at 60 amps gets them up to 14.6v. With a pair of Wet 6s at say 220AH, it would be at approx. 75%.
the key is how high in SOC do you want to go while running the generator. A 50-80 might take 2 hrs while going from 80 to 90 might take another whole hour.
With that converter dropping to 13.6 for Absorption, it would be better to do 50-80s than 50-90s for sure.