Would you be able to attach a greenhouse to your house?
We did that here in NJ, had it built by a professional builder, placed on top of the garage. The greenhouse works as a heat sink during the indoor season, on sunny days the oil burner comes on many times just as the sun goes down. The heat system is connected through the whole house with well placed duct work. Works great and the increase in oil consumption was negligible. I keep night temps at 60 degr F minimum.