This issue was due to a problem with Ultimate Tag Warrior V.3.14 -- The plugin was adding an empty metatag to posts that had no tags defined, and every time you accessed one of these posted, another metatag was added -- as a result, I had over 370 000 lines (yes, you read that right) of stuff in my database.
The plugin author is aware of the issue and fixed the problem (thank you, Christine!).
Disabling the plugin initially stopped more lines from being added in to the database, but since there were already thousands of lines added, it did not change the performance of opening the panel, which is why it appeared initially that a plugin was not the culprit.
Anyway, this issue is RESOLVED and I want to thank everyone who offered ideas and suggestions here and on #wordpress. Your efforts are much appreciated!