if you make the sides of the box with a transparent texture (cept where the beams are, duh) you could texture the mover rather than using a sheet.
If this is for Ut99, you could possibly make an X out of 2 sheets, deintersect them after texturing, move the red builder brush to the side and "add mover".
If this is for 2k3-4 add the resulting brush then convert to mesh, select the mesh after adding it to your Mylevel package and add it back in as a mover.
G'luck