I have two group 27 Interstate batteries that came new in my trailer. They each have approximately 80 aH capacity, for a total of 160 aH.
Since you never want to discharge your batteries below 50%, I have 80 aH available from fully charged batteries.
Presumably you have the same battery, but only one. You have 40 aH available.
You mention wanting to operate a 30w device for 30 minutes at a time, but you don’t mention how often it will run. Run it twice and that’s 2.5 aH used up. Add to this the efficiency losses in the inverter changing 12v
DC to 120v AC, refrigerator, lights, water pump, and charging your other devices, well it all adds up quick.
And if, egad!, you run the furnace for heat, the blower is a real power hog.
I don’t know how many watts of solar you have, so it’s hard to say if it will keep up with your demand and recharge your battery during the day.
Upgrading your inverter isn’t going to give you any more amp hours to work with. It may or may not be more efficient than your current one, but it won’t make a noticeable difference.
Adding a second battery will give you more amp hours, but it won’t help your recharging rate from the solar panels.
I still think a generator is your best solution.
I have a Honda. It is very quiet. It is very fuel efficient. You could probably achieve your boondocking goal by running it for a couple of hours in the morning and a couple hours before bedtime. Try to do your heavy electric stuff while it’s running.
I read good things about Champion generators, but have no real experience with them, so I cannot personally vouch for them. From what I’ve read they are quiet, but not as quiet as Honda.
Many people will tell you to do a power audit to see how much you’re using during the day. You’ll need a good battery monitor to accomplish that, which is another expense. I installed one, and mainly use it to see my percent of charge. I tend to just run the generator and not worry about how much I’m using.