Line up the lexan over the CP. Use C-Clamps or visegrips and a cloth to hold it in place. Then, if you're going to use carriage bolts to hold everything together, drill those first with a regular bit, or if you have it, score the pilot holes with a Dremel. Then secure the carriage bolts tight and remove the clamps and drill the button holes with the spade bit. Just push down firmly and squarely, and go slow as to not melt or crack the plastic.
Its really not that hard to drill through one sheet. I used a set of Ti bits and a single spade bit.