Our house is located in southern Minnesota near Rochester. When we purchased it, there was a 16x16 three season addition. The addition has a sliding glass door and three windows on each of the other two walls for a total of 6 windows. The slider is large and has one moveable section and two that are not. I think it's around 9 feet in width. Last winter we simply left the fan on and door to the room open. It didn't work that well. The windows got frosted up and dripped when they melted off. Last winter was a bugger here....

The addition is constructed on piers. The floor is insulated, but is only 6 to 8 inches off the ground. The building permit file at the City shows there is a barrier between the ground and untreated wood. Normally, 18 inches is required without the barrier I'm told.

The previous owner did not install any heat runs to the addition. They used a eden pure electric heater in the room. I checked their electric bills vs. ours and they were paying over $100 per month more in the winter than we do. Makes sense, I can't imagine a portable electric heater would be terribly efficient.

Given the difficulty for access below the room, what options make sense for heating? I've found the following, but don't know if one is better than another:

1. Electric baseboard heat - simple to install and costly to run
2. Freestanding gas stove (fireplace) - more expensive to install at about $2,200 but more cost effective than baseboard. Also, there is an aesthetic value to it as well
3. Mini-split system - I see systems online for about $1,000 plus installation. Will these work in cold Minnesota? Added bonus is the AC unit, but we haven't really had an issue with that.
4. Install heat runs with returns. I don't know if this is possible or not considering the very tight headroom.

Any other ideas? Thoughts on those I've mentioned?

I've even considered excavating around the room and installing a foundation. Likely it would be a wood foundation on concrete footing. The problem I have with this idea is how to get the 40 cubic yards of earth under the room out. This would create a crawl space under the room. Too bad the previous owner didn't spend a couple dollars more and do the foundation right. It wouldn't have been much.

Thank you for any input