I too have the same problem (SS2.3.0)
One of the pages in the API documentation mentions that you can only have one global instance of the TinyMCE editor but I have tested a DoubleContentPage type that had two HTMLEditorFields on the Root.Content.Main tab and it worked flawlessly.
I also modified the HTMLContent widget, changing the HTMLEditorField to a TextArea field, and I could then add it to the widgets section and save text without issue (obviously no TinyMCE editor). I then changed the TextArea field back to a HTMLEditorField (in HTMLContentWidget.php) and got the TinyMCE editor when I refreshed the page. I can edit, save and publish BUT for some reason the TinyMCE editor is not editing just the TextArea but the stuff immediately arround it.
As a comparison between expected and actual behaviour see the attached picture. There is a Content field on the Root.Content.Main tab, it has a label above it and a grey box arround it. On the Root.Content.Widget tab I have an HTMLContent field but instead of the TinyMCE editor just editing the contents of this field it also allows me to edit the label and I get a field within a field. The only thing HTMLContent should contain is 222222222222222222222 but as you can probably just about make out is also contains the HTML paragraph tags, the grey box that should *surround* the editor and the field name.
I guess this might be caused by a lack of, or too many of, the right identifying tags that the javascript that adds the editor hooks into.
Don't have any more time to spend on this now, but this may help someone solve it; ultimately I think this will need to be fixed by the Silverstripe team. To get round it I may use a modified version of the Random Content Widget that displays all child pages rather than one random one. This may be nicer from a user perspective because it avoids having the TinyMCE editor stick out of the side of the widget box (see screenshot), although I'm sure that's fixable too.