In case anybody else runs into this and searches the forums, I was able to find some software that helped.
The pay version of netfabb is able to automatically repair the model into something usable. That version is quite expensive, but you can use the automatic model repair tool in the cloud here for free: https://netfabb.azurewebsites.net/
After uploading my STL there and downloading the fixed version, it still looked like the house but other software was willing to work with it. Blender was willing to do boolean operations and such. In my case I needed to slice my model so that I can print it in pieces.
The model was still quite usable for Makerware to slice. It looked fine when imported, but resulted in weird shapes in what would be built. The free version of netfabb basic was able to fix this and make it 100% printable.
Note that for commercial use the netfabb software and online service is not free.
penguinism's post in STL Export - fix the models? was marked as the answer