Reading your initial post and the conditions you describe, I'm surprised you got 36 hours before things started going dead... Why? I'm guessing your current batteries are a pair of GP24 FLA or possibly GP27FLA batteries??? When you first arrived and disconnected the trailer, I'd suppose you "hit the level button" and the trailer leveling system went to work. Then, you extended all three slides, then turned on the furnace. You also said that it was "pretty much overcast the entire time.
I'd make a SWAG that when you got the trailer set up, leveled and the slides extended, you likely had already used half the charge in those two batteries. Then, over the next 36 hours, the furnace and the normal battery drains (lights, TV, exhaust fans, refrigerator control system, etc) all contributed to using significantly more power than the roof panels could replenish on a cloudy day.
Looking at a 220 watt solar panel, you'll NEVER get the full "rated output". Why? Panels are mounted on the roof and the sun only hits them "squarely" for a few minutes daily, then every cloud, every tree branch, every raindrop all work against the solar panel to decrease that "maximum of 220 watts"... Often, on cloudy days, you may not achieve much more than 50-100 watts output.
So, a generator is a "must have" on a small solar system for cold weather camping. We have two Champion 2000 watt generators. In the winter, we take one with us to keep the batteries charged. In the summer we take both, parallel them and we can run ONE 15K BTU air conditioner to keep the trailer cool enough to stay comfortable until the sun goes down the the temps cool enough to open the windows and enjoy the evening cool breezes.