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.
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.