Without investing some $$$ into this venture I'm afraid your genny will have to run many hours daily increasing in runtime as the days go by. A second battery ($90), upgrading WFCO converter ($200), converting to LED lighting ($50-150), and/or purchasing a portable 40 amp smart charger ($125) can all play a part in effectively reducing generator runtime.
Camping off the grid for extended periods shouldn't be taken lightly as it could significantly diminish the quality of the camping experience. Additionally you may find that you enjoy this type of camping (you already have a genny) and further investment will yield improved results when doing so. We prefer this style of camping and our first step was to add a second battery (there's always room somewhere for it) which gave us more time between charging cycles via genny. Sounds like a great trip ahead, here's hoping it all works out and everyone has a wonderful time.