Importing Sketchup DAE files into Unity- Lighting issues

I have been creating models of building in Sketchup, non-pro version, importing them into Unity 5 personal. Before I begin, yes, I know that Sketchup isn't the best choice for Unity, but circumstances dictate I use it for many of my models. When I import the models into Unity, they look fine until the camera starts moving. Black areas then appear on the models, the contours of which appear to be following the geometry of my model.

I have tried exporting as DAE and then importing into 3ds max, welding overlapping vertices, and exporting as an FBX, as well as downloading the pro version of Sketchup and exporting as a FBX straight from there, but nothing seems to be working. The only way to "solve" to problem I've encountered so far is to turn off "cast shadows" on the buildings, but as, in the game, the buildings are enterable, this isn't a viable way to solve my problem.

In this picture, the building appears to be in shadow although it is receiving full light. As soon as I moved the camera, the dark area disappeared.

These areas appear very briefly, disappearing or re-appearing with every movement of the camera. Any help or advice on how to resolve this would be greatly appreciated.