My suggestion would be to somehow, efficiently, move some of that hot basement air up to the living area. Maybe some well-placed duct work, with a low-velocity fan? Just guesses, so you might want to Google "heating log homes," and see if anything meaningful pops up, or try to get some ideas from a heating specialist.
I lived in a log house in Colorado for 5 years, and loved it. Heat was provided by a main floor propane stove, and 2 electric baseboard heaters in the basement (that we only turned on 2 or 3 times, total). Our yearly gas bill was less than $1200, and the place was always comfortable. Had a ceiling fan in the main level, but rarely used it. The stove's radiant heat just moved around naturally, and kept everything quite comfortable. The cathedral ceiling consisted of 4 x 6 tongue-and-groove pine, covered by a layer of plywood sheathing and a raised-seam metal roof. Even the coldest nights were cozy (we lived at 8000 feet elevation, had 8'+ of snow in the yard at times).