Geesh, Its not like you are in Minnesota or something... I would FORGET about anything ventless, I don't believe in using something that if it fails, you might die. I bet that your money would be MUCH better spent insulating your house. If heat is costing you that much in Georgia then I would bet your house is not insulated, or could use more. Check your attic, what is in your walls? Maybe I'm wrong, but worth knowing.
What is your kid's bedroom like once the woddstove has been on for a few hours? Does it only get too cold after the fire dies? Is your thermostat anywhere near your woodstove? I'm thinking that you might just let the furnace come on at 3 in the morning, if that is the only time that it is bad, unless the stat is so close to the stove that it doesn't come on in time. It sounds to me like you could really benefit from doing a retrofit to create an upstairs and downstairs zone for your furnace. THis is a whole separate topic, but this guy might be able to help you: http://www.jacksonsystems.com/zone_one.html Feel free to email him, he is very responsive.
My thoughts on vent free: http://220.127.116.11/wwwboard/messages/51478.html and in my followup to that post.
If you are stuck on the closing vents idea then don't close more than two or three downstairs, max., and do this as far back along the supply branch as possible, where it comes off the main supply there should be a damper. Closing off registers in the rooms only causes back pressure and doesn't help very much. I'm really not clear on what you were trying to accomplish by closing the registers anyway...