Hi. You should try a carbide bit to drill the hole. They can't tolerate much bending/walking, so make sure to use a decent drill press (Dremel's piece of crap doesn't count) and go really slow. Maybe split it into 50 passes to drill through, and use water to lubricate/cool.
Also, to keep the drill bit from cracking once it reaches the other side, you might want to clamp a small piece of wood beneath the drilling area.
It helps to have a pilot hole. You might want to start with a 1/16" carbide bit.