Hi,
An update:
I had a certified mobile tech come out and check the furnace. He took it completely out and we both looked over the heat exchanger. No problems found. He did a thorough cleaning of the unit while it was out.
He did find a wasp's nest in the exhaust port, and said that could have been the problem. When he reassembled the unit and we tried it, it gave a "dusty" smell, like the first time in the season. It was nothing like the exhaust smell. He said that it should go away shortly, but I still have about 60% of the smell today.
I suppose the wasp's nest could have been the issue. I figured they had all gone south for the winter. ;)
Thanks!