Would solar air panels be out of the question? I cannot see an insurance company negating them, especially if they were passive in design. There would be absolutely nothing that could go wrong. No electrical shorts, no high heat elements to possibly start a fire, no fireplaces or wood burning to cause sparks to set off your stack of wood on fire, etc.. Just nice toasty warm air on good solar days.
As fas as what is more efficient, all the factors would have to be considered, the cost of the fuel vs the efficiency of the device using it. What may be cheaper in one area could be more expensive in another.
Here for example, propane would cost more then resistive heating, but that would be more expensive than natural gas heat. This is based on the fuel costs, not the cost of the heaters.
I use two kerosene heaters in my shop/garage to bring the temp up to comfortable, and have a natural gas heater to maintain that. Other wise I do not heat it when not in use so the only heating is from a limited solar gain.