We have a laser with a bed that big. Challenge is going to be thickness. The laser gives a conical cut. You could cut identical 1/4" sheets and then stack/glue them after cutting. You could use 1/4" ply as the back, saving some weight.
[EDIT: Ask the laser experts … you might want to focus the laser partway through the depth to get the best cut on something thick]
The Tools page of the wiki is a good overview that points you to specifications and information about most, if not all, of the major tools that we own.
It is linked from the upper RH corner of the main wiki page.