Can you driveway camp for a week? Live in it and see if the battery lasts the full week. If so, use a meter to see how much is left at the end of the week.
I have a group 31 AGM battery. It is more than enough for a week - I barely put a dent in it over 4 days. I have no need for solar or generator. Before I went with a generator, I would simply add a second battery.
You might find that your fresh water and dump tanks are what limits your stays the most. How much fresh water do you have left after a trip currently? Does that equate to being able to go a week without a refill?
How much do you fill your dump tanks after a trip currently? Will you be able to go a week without needing to dump either?
For me, I could push out the water to about 10 days max with frugal use. So, increasing my battery power isn't going to keep me out longer.