Idea I had for protecting birdhouses I have not seen elsewhere
What about enclosing each birdhouse in a cube of grids? Many people are using powdercoated metal grids now to make guinea pig cages, they are storage grids meant for building shelves for closets, the grids are 14" square with openings that are 1 1/2". It is easy to make a cube using zip ties although they do sell hard plastic circular connectors.
If the cage was inside, squirrels and cats could not get in. The cubes could be suspended from trees. Of course you could still tailor the actual cage hole size too.