I ended up making a U shaped frame with a crosspiece in the middle like this (overhead view):
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The monitor sits on top of that with the glass facing the bottom of that picture. You will need to measure this so the side and front pieces align with the frame of the monitor. I used wood screws and washers to secure the monitor frame rails to the 2x4s. Since the 2x4s are on their sides, this ended up lifting the monitor about 4 inches which turned out to be just about perfect for me. If you need it higher, you could always just use an additional piece of MDF or ply to sit underneath the housing. Once I put the assembly on the shelf, I also added a horizontal brace that runs the width of the cabinet and secured the top of the monitor frame to it (just to keep it from swaying forward/backward if the cabinet is moved. I hope this makes sense. Let me know if not.