Later that day I found out what was interfering with the smooth removal of the evaporator core. As Matt said, it was the black goo, but some was in an unexpected and unreachable place. There was some that was still around the inside edge of the A/C box. When I scraped more carefully around that edge the core moved more freely, but it still wasn't entirely easy. I pulled harder and it did come out. There were two rectangular spots of black gleck on the back end of the unit gluing the foam surround to the inside of the A/C box. That seems unnecessary since the unit has such a tight fit anyway. I will attach a picture of this in case it is helpful to anyone else doing or thinking of doing this job.

One has to be careful about the side of the Evap core hitting things like the ends of the A/C lines that come through the firewall and the cable bundles there near the ECU computer. And the right windshield wiper arm was also in the way. I ended up with some small areas where the edges of the foil-thin aluminum fins were flattened. I tried straightening them out with a butter knife but the results weren't the best. Quite tedious. I decided to order a new one since they can be found through Amazon for about $100. I used the old one to practice insertion and removal. Even with the above mentioned items moved out of the way it is still a bit tricky to get it in and out without flattening some of the fins.