The majority of my camping is boondocking, though in Southern California deserts, not Illinois so some of my suggestions may not apply. Do be aware though that while we all want to help, we also find it very easy to spend your money for you. So take the suggestions, even mine with a grain of salt and consider if it really makes sense for you at this time. Also I am a pretty frugal guy, but I realize that cheapest is not always best.
First and foremost I would do absolutely nothing, make no modifications and just go dry camp and see what happens. It's summer, it's not like you're going to freeze to death overnight if the battery dies or the furnace quits. Bring an extra blanket or sleeping bag and go see what happens. Worst case every system dies and you're still in a large comfortable tent (toy hauler).
If you decide to replace your battery, and you have room, then by far the most cost effective replacement for a capacity boost is two 6 volt batteries from Costco or Sams club. Around here everyone I know is a Costco member so even if I wasn't, I could easily get my neighbor to go with me to buy batteries if needed. Trojan 6 volt batteries are nice, but they add to the cost for very little in performance increase.
6 volt batteries are wired in series instead of parallel like 12 volt batteries. What that means is you will have to add a single wire between the two batteries. If you have any 8 gauge multi stranded wire around the house that is good enough for what you are doing. You can also go to Walmart or the auto parts store and buy a short battery cable with a ring terminal on either end to connect the batteries.
How to wire batteries in series. Ignore the disconnect if you do not have one.

How to wire batteries in parallel.

You can add LED lights to conserve battery power. I did, but I also ran for years on my normal incandescent lights without a problem. Feel free to use your lights as needed. Just don't turn on lights for no reason and leave them off when not needed and you'll be fine.
Your propane refrigerator still needs 12 volts from the battery to run the circuit board. Definitely use your refrigerator, but pre-chill all the food in your home refrigerator and turn on your TH fridge the night before loading. If you have a cooler load it with ice just in case the fridge dies (which truly it won't unless the battery dies)
The air conditioner is out of the question unless you run the generator.
Most toy haulers have large tanks, I only have 40 gallons of fresh and can make it through a weekend. Just don't waste water and you will be fine. Take navy showers.
- Get wet including your hair and turn off shower head.
- Soap up head to toe.
- Turn on shower head and rinse off.
- Shut off shower and get out.
For washing dishes many people use plastic tubs in the sink, one for wash water and one for rinse water. I do it differently and use running water to rinse the dishes as I feel it gets them cleaner. But only turn the faucet on a little bit. The stream should be maybe half the thickness of a pencil or less. Turning the faucet on harder is only wasting water. Also I use a lot of paper plates when appropriate (not going to use paper when eating a steak for example) so I'm mostly washing things like a spatula or a serving tray etc.
As the weather cools and you start to run the furnace more you might start wanting to use the generator to charge the batteries. Find your battery charger on the TH, it is probably behind or under the fuse panel. Let us know the make and model and we can tell you if it's worth keeping or replacing for charging on generator power. If money is tight and it's not a good charger but you have a decent charger in your garage you can bring that one along and run it off the generator.
Water heater isn't going to impact the battery much, won't really affect your propane usage much either. But I only turn the water heater on in the morning then turn it off once hot. The tank will stay warm all day and sometimes all night. So unless taking a shower the water heater is mostly turned off.