I doubt that zinc heated to room heating temperatures will have any odor, since virtually no zinc atoms will be liberated.
There is a condition known as "zinc fever" that is known to welders. That's because galvanized coatings, heated to welding temperatures, causes zinc atoms to be liberated. If inhaled this can cause one heck of a headache, or so I've read. Excessive fumes can also cause lasting neurological problems. This is why most items that need both welding and galvanizing are welded first, and then galvanized.
Welding temps are above about 1300 degrees F. A home furnace might heat its ducting to about 200F. Nowhere near the "danger zone".
As for the aroma you detect in forced air furnace heated homes... some of it may be dust that is burnt by the heat exchanger. Usually this happens at startup in the fall, when dust that has settled back into the system through the air vents is heated. It goes away after the first run. If it continues, the furnace filter may be leaky, clogged, or too coarse. I prefer to use 3M Filtrete electrostatic pleated filters - while not HEPA, these can actually clean the air of dust, pollen, even some cooking odors.
Stainless steel is not only more expensive than plain steel, but it's also harder to work. My Neptune dryer also has that bluing caused by new jeans... for me it's not a problem, although I'd prefer it if mfg's went back to good old porcelainized surfaces instead of this new fangled plastic paint.
I agree that a stainless drum looks nicer than a painted one... but... functionally I don't think it makes much difference.