Move Ctrl + F6 or make a macro that mimicks what Ctrl + F6 does

Ctrl-F6 and Alt-F6 both switch document windows. I can use either combo with one hand...

You could use:

Sub ActivateNextWindow()
Dim i As Long, j As Long
i = Application.Windows.Count
j = ActiveWindow.Index
With Application.Windows
  If j < i Then
    .Item(j + 1).Activate
  Else
    .Item(1).Activate
  End If
End With
ActiveWindow.WindowState = wdWindowStateMaximize
End Sub

Alternatively, if you have a programmable mouse with an extra button, you may be able to use its config app to use that button for toggling the windows.