Before I went too far in trying to figure out the problem, I'd pull the shroud and check for wasp/dirt dauber nests on the fan blades. If there is a serious vibration, this is the most likely cause. When I fired ours up for the first time this year, I thought it was going to shake off of the roof. Ten minutes later after removing a good sized dirt dauber nest, smooth as ever. Would have been five minutes, but I took the opportunity to spray the coils out good since I was there anyway.
The air buffeting could be caused by the vibration since it transfers to the squirrel cage also since it is all one shaft, but it is probably just a design flaw in the duct system.