Another approach to consider...
Go on ebay and find mirrored plexiglas; it's typically 1/8" thick. While you're there, get a clear plastic display case or two.
Cut the plexiglas the same length as the base, and about 3" wider (some experimentation might be required, based on the height of the display case) than the base. When the plexiglas is installed on the inside of the case (strictly on a temporary basis, no cement should be used), it will be at an angle. Setting the model on the top of the case, which will allow the underside of the model to be seen via the plexiglas mirror.
Several advantages to this approach:
Transporting the model is safer, because it's in the case while in transit. At the contest, remove the model, insert the plexiglas mirror, place the top on the base, and set the model on top of that contraption.
Your model will stand out, because it is higher off the display table and can catch judges' eyes more easily (psychological stuff).
There should be no need for the judges to handle the model in order to look at the underside because of the mirrored plexiglas.