Someone posted a great reference pic of the tri-viewer online at the RPF that included a profile view of the stand. I took it into photoshop, and adjusted a little bit for parallax. Not perfect, but enough that it's square enough to import into Illustrator.
Once there, I added to my drawing the base, and also the top pyramid. In my drawing, the base is the right height and the profile looks good, but this drawing does not properly show the shape of the base. I'll put together a drawing later that shows this.
For now, I am feeling very happy with this drawing. It appears to match up to screen reference, and "feels" right.