I'd call the Grand Floridian and ask to speak with someone in the bakery. Explain that you saw the special on Food Network and was interested in purchasing the small cakes.
I would think, though, that it may not be possible. Here's why. If you noticed, they baked a very large cake to make the individual ones. They actually split a layer of the cake in 1/2 or 1/3rds then assembled the individual cakes in a ring mold. This is a lot of work. It may not be cost efficient for them to bake a whole cake for one or two mini cakes. But I don't know the policy and how things operate in the bakery. As with anything else, it is absolutely worth calling about!
Besides, the (wedding) cakes from the GF are absolutely decadent. I ordered an anniversary cake for my parents in 2001 with the yellow cake and white chocolate mousse filling - it was TO DIE FOR! And they decorate soooooooo beautifully!
Please post when you find out about the mini cakes.........thanks!