I use a coping saw all the time on trim. It is the best way to get a tight joint on an side corner. A coping saw would be a poor choice for this project though.I remember cutting trim with a "coping saw" In the 50s. Don't think anyone uses them anymore.
Sabre saw is another name for a jig saw. The oscillating saw would be my choice as well. Once you own one, you'll be surprised how many jobs around the house they are perfect for doing.
You could do this by cutting down the middle of the piece of particle board with a jig/sabre saw and muscling it out. But any project worth doing is worth a new tool, especially one as handy as an oscillating saw.
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