Are you sure it's your furnace or are you losing a massive amount of heat somewhere? A newer furnace will be more efficient but in the end, how much heat your home loses affects how often it runs. Tearing down all your drywall is certainly not the best answer but you can start by shrink wrapping older windows and making sure seals around doors are doing there job.
I live in an older condo and thanfully I only have 2 exterior walls but the furnace still runs quite often on really cold nights. I know in my place it has less to do with the furnance and more to do with the insulation in the walls. I'm sure if I were to start opening walls the insulation would be wafer thin and saggin in a lot of places.
New furnace is great, will save you some money, but the bottom line is if all that heat is escaping your house the furnace will still have to run a lot.
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