Step 1: The transformer (core)
I used a pipe cutting blade (hacksaw blade) on a reciprocating saw to cut the secondary off the transformer core. Near the end of the cut I had to use extreme caution as I did not want to damage the primary coil. The primary and secondary can be identified by the number of turns and the gauge of wire. The secondary has many thousands of turns and uses hair thin wire. The primary is more like 18 gauge.
Once the secondary coil was cut away I used a short metal bar and a hammer to pound the trapped portion from the core. It was wedged in there pretty good. I cleaned out everything except the shunt and the primary.