I think 3 to 4 months between recharge will be fine as long as they are actually disconnected.
Size of the generator will depend on the converter. If the converter rating is 35+ amps you probably need the 2000 watt. 35+ is the converter rating not the RV plug rating. Post the converter model number for best answers.
If the converter is good you will get about 14.4 volts charging and the top up can be done in 2 or 3 hours. If you have a fixed voltage converter or a WFCO that often acts like one you really should charge 4 to 8+ hours.
OK to use a portable battery charger if you have one.