Screw problem
Well - you wouldn't need to drill past the head. The goal is to eliminate the side of the head or anything larger than the threaded section of the screw.
there are really only two approaches because the transmission - tranny - box is plastic. you can A) either use some sort of cutting device to make a slit for a screw driver or try and cut out the screw from the top down.
What sort of tools do you have and how big of a screw head are we talking about? Smaller than a pencil eraser head?