The material had flowed completely around the head so even when I heated it up, it did not soften enough to push the material out of the gap behind the nozzle. This gap is needed for the head to move up enough to remove the print core. I ended up having to take the printcore out with the bracket it slides into. Then I had to use Acetone to melt and chip away the PC material enough to remove the core from the bracket. There was no way to do this without destroying the printcore.
So, although I destroyed the print core, I was able to get the bracket out and reinstalled into the unit. The next issue was leads to the fan and the sensor/shield on the head unit were pulled out of their contact holders when I had to pull on the core and melted PC material. I tried to solder them back on, but as soon as I did the contact must have gotten too hot and it fell off of the senor board.
So, it looks like I need to get a new core and also a new cover/sensor/fan unit. Ultimaker was very helpful with getting me these new units and I should have them on in (2) days. I assume once I install these new parts everything should be back to normal.
I'm still not sure how this occurred though. I had done the same print 3x before without an issue.