Well you could build it like my icecream cake. I used a steal plumbing pipe from the hardware store with a flange attached to a piece of plywood. Then cut pieces of PVC pipe the same as each layer.
Stick the pvc into the cake. Clean out the cake from the PVC so you can slide it over the pipe. Then place the next cake. Use the acrylic wilton boards without the flanges on the bottom. So its just a plate. Drill a hole in the center of all those the same size as the pipe. Then just slide each cake over the pipe. I'm not sure how you are doing the letters but I would do as stated above and make them out of styrofoam. Also the bottom tiers are moved in enough but the ones above would need to be moved in more for my plan to work. Also the bottom of the plates will show since they are white so you have to find a way to cover them.