Its a real problem, as we were in the identical situation as you for years, until the only space opened up with a 30A receptacle. I had to replace my house batteries as they went dead.
First, you will have to disconnect the negative battery cable so you don't drain your batteries. even with the house battery disconnect switch 'open' or off, you will drain your batteries due to parisitic loads from your inverter/charger. Next, once every couple of weeks, reconnect the battery cable and run your gen for 2 or 3 hours to partially recharge your batteries. even this way, you will not get your batteries into 'float' or fully charged, as the 'absorption' phase takes hours. After doing this a few times, you may be able to stretch out the interval between charges to 3 weeks or so. It's really not a good solution. Now that we have a 30A hookup, my battery problems are over. Don't forget to do your gen maint (filters, oil change) as you will be putting hours on your gen. Good luck!