Your single Honda 2000 can run a 60 amp Non-PF corrected charger or a 75 amp PF corrected charger. It will struggle with a higher amp non-PF corrected charger.
If your inverter-charger has (typically for a 2000w inverter size) a 100 amp PF corrected charger, the single Honda 2000 will struggle badly, especially at any altitude.
So that limits your options to a 3000 or a pair of 2000s. You get more power from the two 2000s and they are handier physically to deal with going camping. Both 2000s will make more noise than the single 3000 if the difference there is an issue.