You could try adding the "paste" plugin to tinyMCE. Documentation is
The file to edit is tinyMCE.ascx in the admin folder. There's already an existing "plugins" line of code. So you could just add "paste" to the end of the comma delimited list of plug-ins.
Then you may need to add the "pasteword" toolbar icon (documented at the same link) to the toolbar icons already being specified at the end of "theme_advanced_buttons1".
I'm not sure if just adding the "paste" plugin is enough, or if after adding the plugin and toolbar icon, you may need to click the new Word toolbar icon to paste your Word contents into the dialog window that opens up.
I haven't personally run into this problem, so I don't think I can test it on my end. But maybe see if this plugin and toolbar icon help.