I've played around with a fresnel lens years ago. Pretty amazing. It will vaporise a penny in nothing flat. Walk across a dry lawn and leave a flame trail behind you. From what I understand you don't gain anymore energy from them except what the total area of the lens equals. Meaning if the area of the lens is 9 square feet it would gather the same heat as a 9 foot square solar collector. The lens only condenses the total energy into a much smaller area. Would be interesting to test but tracking the sun would be a challenge.
A lens will collect all the incident light and focus it on something (maybe a pot of water or some other working fluid.) The conversion efficiency is the secret key to solar power. I'm not up to conversion efficiency with solar panels, but I don't think it's above 10%. Thermal efficiency of conversion using a working fluid is like a power plant, could be as high as 40 percent or so. As you say, tracking is tricky but it has been done, with problems, of course. Ivanpah Solar Power Facility - Wikipedia
For a cheap entry into fresnel lenses, try a pack of these. Use to squint at the dates on coins, start fires, whatever comes interesting. I have one in the desk, one in the kitchen two in the camping supply box, one in the BOB and a couple spares. Just found them again on Amazon the other day. https://www.amazon.com/dp/B07Z88T25X/?tag=survivalmonke-20
I've skimmed this thread and hadn't seen insulation mentioned. I've never been in a well insulated trailer. Sealing cracks and adding more insulation would reduce the heat loss and make the space more comfortable. Do keep in mind that a sealed space will require adequate ventilation if you burn anything to produce heat. (I imagine a snow cave here. So well insulated it can be heated by a single candle, with down slope air inlet and roof exhaust.)
Don't overlook a humidifier. Keeping the humidity around 50% will reduce evaporative cooling of the skin and aids the respiratory system. Makes a big difference in the perceived warmth of a space.
I never thought about the perceived warmth on the skin, but there was always a kettle of water on the wood stove up home. The benefit I saw was it kept my nose from cracking inside in the dry winter air. No worries around here. It was 74 yesterday.
I should start looking for a big screen TV lens. Doesn't take up much room and is tremendously fun to play with. A few times during the winter I have fired up the furnace and spent some time in it. Doesn't do to bad. I have tried my best to seal it up pretty tight. For long term use a cover would be a must. I purchased a couple giant tarps years ago just because the price was right. Pretty sure both would cover it. Last year I made a trade and scored around 300 pounds of very thick, large, UV resistant plastic. Black on one side and white on the other. I believe the stuff is used to cover grain. Very good idea on the humidity.