The reason it won't rotate in the Project environment is this:
As a generic model, you have used extrusions and sweeps and stuff that is all modeled/hosted on the Level or other Ref.Plane, and either way is related/hosted to a LEVEL. So when you plonk it into the Project on Level-1 or whatever, that's what you get.
Think about it...can you place a furniture family in a floor plan and then tip it up on its side? No, you can't. It's base is always and only parallel to the Level that it's hosted on.
You'll either need to build everything at the angle you want inside the family before you bring it into the Project, or build everything based on a reference line that's got an angle parameter to the Level so that you can tip it all up based on a parameter, or use a more complicated solution like an adaptive family.
OR...
Use a face based or wall based family so that you can place/host the facade onto the outside of an actual wall element (or a ref.plane, or a grid line, etc.) and then you can rotate it in an Elevation view.