How do you store your built models for long-term display?
This may sound odd, have you considered using an upside-down fish tank? I've actually seen this used in the past after the former occupant died. It was only a smaller model on a baseplate, but the width of the glass for the tank managed to fit inbetween the studs on the baseplate and worked quite well. Granted, stacking them could produce an issue, and you might want to try plastic tanks instead of glass ones but depending on the size they might start quite cheap.

Something like this (but upside-down, and not containing fish):

Image from http://www.flickr.com/photos/nigelguy/4208026780/in/pool-lego/