I will never trust online reviews for any home improvement services. Made that mistake when we had a new roof installed a few years ago. Picked an outfit with great ratings, only to have them royally screw up the job. To the extent of things like using illegal shingle fasteners, lots of shiners and broken shingles everywhere, to having an employee urinate in the yard while my wife was looking out the kitchen window at him (just 20' away from our well), the first day on the job. But I digress.
The quote for $13,000 is unrealistic. For considerably less than that, you can get a new high-efficiency, forced air gas system installed. My sister did the same in her 90-year old place in Wisconsin a few years ago, and her winter gas bills are a tad over $130 a month. Her old system had the huge gravity-feed ducts, which the installer ripped out and replaced with modern ductwork. I think she paid less than $6000 for the system. I removed her old chimney for her, as it was ready to collapse anyway, so she dodged a bullet there. As others have said, her new furnace uses just 2 small (intake and exhaust) PVC pipes venting through an exterior basement wall.