I like both Alex's and Chuck's ideas, and came up with this rough, not-even-remotely-to-scale sketch on my iPad. (In my mind, the visible parts of each stage of the trophy would be roughly equal.)
What I envision are three extruded shapes nested inside each other--square and round tubing is abundant, and finding triangular extrusion can't be THAT hard. The exact sizes of the tubes can be adjusted to suit the significance of the award, and the trophy could be made to (dis)assemble by use of set screws in the back; wrapped in tissue paper to protect the finish, the pieces should be able to nest in the square to make shipping them more compact. (As for finish, I'd want some expert opinions--anodizing anything in white appears prohibitively complex, and thus likely expensive if my Google-fu is strong.)
The blue bottom member would carry the FRC logo, while the award name and event could be engraved on the red top piece (perhaps turned 90 degrees for space). I believe engraving the red piece would make the trophy more visually appealing, though if cost savings ruled that out I'd suggest to rotate the square 45 degrees and engrave the FRC logo and award on adjacent sides. To save FIRST from wasting a bunch of engraved pieces on relatively rare four-team alliances, the policy becomes that the alternate team and the team it replaced leave the venue that day with one trophy each; the money FIRST spends on shipping the second trophy to those two teams will almost certainly be less if history is any indication.
I encourage anyone who actually knows what they're doing to chime in with feedback.
