Sorry for the late response to this, but one thing to be aware of. Since this cutting is being done with a round bit spinning on it's central axis, the corners of your boxes will not be square. They'll be pretty close, but not exact. In fact, if these squares are cut with the carving bit, then the squares will be slightly wider at the top than at the bottom because the bit is taped. In order to get straight edges, you'll want to use the 1/8" cutting bit and use a series of overlapping rectangles to cut out your space which would also probably be faster than using the carving bit anyway. That will unfortunately leave more of a round corner than the 1/16" carving bit, but at least the edges will be true vertical.
I haven't looked at your model, but I've assumed that you created a rectangle and then used the carve region option.
Just a heads up, though a bit late.
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// Matthew
// "When all else fails, follow directions."
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