CKEditor oEmbed Plugin Shows up in config but not in actual Editor instance
I figured it out. On the Drupal side, everything was configured correctly. The error was in the Javascript. The original plugin.js file has the following:

editor.ui.addButton('oembed', {
                    label: editor.lang.oembed.button,
                    command: 'oembed',
                    toolbar: 'insert,10'
                });


I modified this to 

editor.ui.addButton('OEmbed', {
                    label: editor.lang.oembed.button,
                    command: 'oembed',
                    toolbar: 'insert,10'
                });


Note the name passed to addButton() from oembed to OEmbed. I think there was some conflict in naming it oembed, possibly from some existing functionality. Not sure, but that was the fix for me.

In addition, I should note that for the Basic Editor, I had to modify the HTML filter to allow tags that the oEmbed plugin added to the source view. Hope this helps someone.