[CeeTeeX5]

Here's what I would do.

1. Tape the pedal in place with either masking tape or you could use some double sided 3m tape on the back.
2. Drill a pilot hole about the size of the shaft on the screw (diameter excluding the teeth on the screw). Go maybe one size smaller on the drill bit.
3. Install one screw to see if it gets good enough grab without cracking the plastic
4. If all is good, drill the rest of the pilot holes and screw it in

Or you could you just use the 3m tape solely.

Nice looking pedals!