I personally see no reason why you can't leave the stove operating while not home. I'll let the alarmists give you their gambit of reasons as they disagree. Of course there are reasonable precautions you need to take. The major one is not to leave the house with a raging fire in the stove and not to have clutter and combustibles near the stove. Another precaution would be to keep the chimney cleaned. Use the stove for several weekends while you are at home so you get acquainted with the characteristics of the stove, loading intervals, heat ranges, etc. One thing you will experience is a downdraft or back puff into the house while you are not home. That means you won't be home to clear the house of the smoke smell. In 35 years of burning a wood stove 24/7 in the winter time, I have had that happen only 3 times and it was my fault, from putting too many logs in at one time. I wanted to stay away from the house longer and figured if I put an extra load of wood in, it would keep the house warmer, longer, without a reload and then adjusted the air inlets a bit more closed than normal. That caused the gases to build up in the stove and it burned hotter 3-4 hours after I was gone. With the stove hot and the chimney cool, the stove back puffed through the adjustment plates and the smoke smell got into the house. I know this because I duplicated what I had done so I could observe everything while I was home. So that accounts for 2 times. The third time was when the wind was blowing pretty hard, I figured what the heck, I can put a bigger load and damper down more because of the increased draw the winds were causing. Good idea until the wind quits blowing and Murphy's law says it will about 30 minutes later. I was home then and had the fans clear the smell right away. Another down side would be, the room the stove is located in will be very warm but fans can help to redistribute it..

Just a side bar...there are chemicals you can spray, etc. that will get the smell out or neutralize it. An old home remedy that actually works, burn a candle until the smell is gone.

I live in the Md. area near the Appalachian Mtns. We get very cold and snowy winters here although maybe not to the magnitude or duration you may experience. I burn the stove 24/7 (and have for about 35 years) except during my day of frequent cleaning. I average 3-5 cords a year (wood is abundant here) and it heats a 4,000 foot area of the house averaging 68 - 70 degrees. In another area of the home that is around 1800 feet, a pellet/corn stove does a great job. I have an oil fired furnace and my automatic delivery company only delivered 7 gallons last year. Of that 7 gallons, 5 of it went into my diesel tractor. A pellet stove might be an option you may want to look at. If the alarmists scare you, the pellet stove would be your best bet. It has safety devices to shut it down and they do a good job. From what you described, you'd probably use about 50 bags a season until you realize how much you like it. Then you'd go with about 90 bags.

I think if you burn the stove at night it would be better since that is normally the coldest time of a day. You'd be there if an issue would arise also.

You're correct that there are many variables, but here are some things to consider:

A fireplace insert does not heat as well as a free standing wood stove. Most(maybe all) inserts incorporate fans to move the heat out into the living area. In a power outage - the time when you most want wood heat - they don't work very well at all.

One cord is really not very much wood at all. Even with a very well insulated house and a very efficient stove, I do not think a cord would last more than a month, and probably less in the depths of a MN winter.

An insert plus a single cord of wood will reduce your gas consumption, but not to a significant degree.

Whether you're comfortable leaving the house with a fire going is a matter of personal choice. Some people routinely stuff the stove before leaving the house or going to bed. I've never been totally comfortable with this and it also wastes wood - you don't need a whole lot of heat when you're not there or asleep. If you're going to burn wood, however, you will inevitably be leaving the house on occasion with a fire still going and the stove still hot.