I find work well using a jig saw with a special counter top cutting blade. Most blades cut on the up stroke, a counter top blade cuts on the down stroke thus reducing splintering. I always use masking tape as security. lay on the tape and then mark the line on the tape.
Cutting off the L Might be best accomplished by cutting on the back side since the intersection in the L is so tight. Therefore you would NOT need that special blade.
I personally cannot envision using a circular saw on this project as it is so big and your line of sight is so reducted and the cut is soo fast. Consider a jig saw, or short bladed recipical saw or a band saw. May have to devise an elaborate jig system which ever way you go.