He ended up using the reciprocating saw to score the Styrofoam. I went behind him with a chisel and pried it out. No matter what method you choose, be prepared for a mess.
Here is a shot of the walls after the Styrofoam was removed but before I vacuumed.
W cut larger channels where the outlet boxes were so he had plenty of room to run the wires later.
Then we pulled wire from the panel box to each of the boxes. The wire fit right into the lines we had cut out.