Originally Posted by westgoin
To complicate matters, we are sure the fan was installed with the original construction and is attached directly to the cieling beam with no easy access to remove without significant damage to the ceiling. There appears to be no logical path to vent to the exterior of the home without encountering major structural elements.
Generically speaking, one option is to use a remote fan that pulls
air from the bathroom rather than pushing it out, that way your don' t have to be concerned with mounting a fan assembly anywhere in the bathroom, you just have a small grill over the end of the duct, and mount the fan in the attic or at the exterior:
Fantech is one manufacturer of such products.