And if the flue is single wall pipe, it will cool the gasses so much that you may not get a decent draft and will create a lot of creosote. You could mitigate that by burning the stove very hot, but that's a waste of wood, more work to cut it, store it and haul it to the basement, and waste a lot of heat to the outside.
I would use double wall pipe. I already checked prices and found long sections, I believe they were about 5 feet, for just over $100. Am I missing something? Sounds fine to me.