This is not mean to be a review or a complaint. Just a heads up for anyone who might be experiencing this issue.
I installed the Duplicate Posts plugin and proceeded to make two new posts from older posts in the database. One was saved as a draft and the other was published. Everything seemed OK until I tried to publish a brand new post the next day. The Publish button was gone and replaced with a Submit for Review button, almost as if I had lost my admin privileges. After about 8 hours of database scrubbing, reinstall, and general head banging against the desk, we figured out the problem. The plugin itself had already been deleted at this point since it was the most recent plugin installed, so it was the most likely suspect. But the two posts I created were still in the database. So I deleted the posts, and amazingly the Publish button came back.
I don't know if the posts created by the plugin were corrupted or if an interaction with some other plugin caused this to happen, but whatever it was it was the perfect storm of events that resulted in a bricked site.
So unfortunately, I won't be reinstalling the plugin but it did seem to do what it was supposed to do. Again, just a heads up in case anyone else experiences this.