I want this someday too (also live in MN). Wood pellets or just a wood burner are your best bets for secondary heat. I grew up in WI and we only had electric base boards and a wood burner (then pellet stove). Get the house up to 85 before bed and by morning it's in the high 50's and start the fire again. You need to be ok with fluctuating temps to really make it work.
You mention cloudy days but the one positive about our brutally cold winters is that when it's below zero it tends to be sunny out. If you set up your solar to extract as much sun as possible during these times, as well as build your house with large south facing windows with stone or concrete flooring you will not need to heat the house much during even the coldest days (solar radiation will heat the house and the concrete flooring will release what heat it gained in the evening).
You mention cloudy days but the one positive about our brutally cold winters is that when it's below zero it tends to be sunny out. If you set up your solar to extract as much sun as possible during these times, as well as build your house with large south facing windows with stone or concrete flooring you will not need to heat the house much during even the coldest days (solar radiation will heat the house and the concrete flooring will release what heat it gained in the evening).