I just use my tablesaw with a zero-kerf plate, the table saw fence and a push stick. I set the blade height to just a little over half the box height and eyeball the fence to cut about 1/16 away from the surface of the work piece.
I make one half cut, flip the piece, and complete the cut. The phoenix cut up above is what I aim for; the latest cut with the dragon was too close and the saw blade brushed the workpiece.
I think a bandsaw would be a much better choice. Unfortunately mine is currently buried in the back of the garage at one of my rental properties… I need to go dig it and my sanders out!