The premise of "I only have 3minutes and twenty six seconds to perform" is quite common for performers that make guest appearances on television. They give you relatively short time spans to do anything and you have no chance to build any rapore with your host or audience. As a mentalist, it compunds one's task as you have a very limited amount of time to establish what you do.
A book test and a design duplication is the first thing that comes to mind but PK type effects (objects moving, bending, or manipulated. It's Paranormal is a good example of a perfect effect for this), The Borodin Locket (using either Borodin's routine or a modified version of the Koran Medallion), or certain card effects like Kollosal Killer would work well.
I have a few other ideas that I would use myself but are my own signature effects with some of them specifically designed to be used for such spots. The point is that you have very little time to establish one's self and often it is to promote your appearance somewhere. You can't just pull anything off the shelf to perform but instead must chose very carefully. While the classics may be just that, they do not necessarily establish you as a "unique" performer which IS the case as far as the public is concerned. The last thing you want them to think is that you are just another act like the last ones they saw.
Paul Alberstat http://www.mindguy.com