Let's take a half discharged group 27 battery and stick it in a pickup and connect it DIRECTLY to the alternator output stud with six gauge wire. That's a pretty serious setup. Start the engine and you'll get between a thirty and forty amp charge rate - for awhile. If it STAYED at 40 amps, you'd have it knocked - you would only need to run the truck FOR A LITTLE OVER AN HOUR to recharge the battery.
But the charge rate TAPERS. I allow THREE HOURS in my system for the alternator to decently (BUT NOT FULLY) recharge a battery this way. Are you going to drive three hours a day?
"Shady campground sites" are great. But you are saying there is NO SUN ANYWHERE NEARBY? A 150 watt panel and roll of 10-gauge black electrical cord is a formidable charger.
I do not like the idea of having to change batteries. The more you do it, the more likely an "oops aw gee whiz" is going to happen.
You are not going to find an "Aw Shucks The Answer Was A Piece Of Cake" remedy for your needs. Believe me, I am so lazy and such a cheapskate I would have found that answer decades ago. Looking for an Aladdin's Lamp is a waste of time.
You need to take multiple steps starting with NOT RUNNING your heater's fan motor. Find another way to stay warm. Your furnace does not exist when not connected to a "hookup". If you DEMAND to use your furnace, it's going to cost you. Not pennies but sacks of cash. Your choice.
You need to take your pick:
a) Save on electrical usage
b) Spend LOTS OF MONEY and keep using power
Your calculations of energy usage are far off. I think many heaters have fans and solenoids that use TEN AMPERES of battery power. Are there ANY standard lamps out there that use less than 2 amperes. I do not think so. The water pump usage is inconsequential. Then you have a refrigerator at the trough 24 hours a day.
If there was enough room to support a longer (13") battery, this is what I would do. Change the battery to a group 31. Buy an Olympian catalyst heater. Figure out WHICH TWO LAMP FIXTURES ARE ON THE MOST per day and replace them with LED lighting. Step 2 if needed would be that solar panel.
CHARGING WITH THE ALTERNATOR
This is ideal for folks who drive several hours a day between campsites. In order to make an alternator USEFUL for a battery charger you need to do some heavy-duty modifications to the voltage regulator circuit. Sometimes this is impractical if the alternator voltage regulator is interfaced with the vehicle engine control module (computer). Start the engine and the voltage rises to 14.8 AND STAYS THERE. This is too high for the car battery, so a switch is needed and voltage dropping device (rectifier). An adjustable voltage regulator (Like the 911 series TRANSPO or the F540SP model. This sort of stuff is WAY WAY beyond the interest or abilities of the average auto electrical shop never mind an RV owner. So using the vehicle alternator unmodified is a "umm" impractical idea.
PS: You want a WARM blanket? Look at a THINSULATE king size. Way thinner, way lighter, and way WAY warmer than a really thick down comforter. Why king size? Well you can camp in Prudhoe Bay and won't get cold if you fold it in two.
There's more than one way to de-fur a cat
