Ah, figured it out. The object was embedded as a Shape. I discovered this by first realizing that there was a Context Menu item to open the embedded document whereupon I recorded a macro to access it. For the sake of reference, the macro code I got for finding it, opening it, finding a piece of text, copying what followed it, closing the document, and pasting said text into the header is the following:
Code:
If ActiveDocument.Shapes.Count > 0 Then
ActiveDocument.Shapes(1).Select
Selection.ParagraphFormat.Alignment = wdAlignParagraphCenter
With Selection.ParagraphFormat
.LeftIndent = InchesToPoints(0#)
.FirstLineIndent = InchesToPoints(0#)
End With
Selection.ShapeRange(1).OLEFormat.DoVerb VerbIndex:=1
Selection.Find.ClearFormatting
With Selection.Find
.Text = "Document ID"
.Replacement.Text = ""
.Forward = True
.Wrap = wdFindContinue
.Format = False
.MatchCase = False
.MatchWholeWord = False
.MatchWildcards = False
.MatchSoundsLike = False
.MatchAllWordForms = False
End With
Selection.Find.Execute
Selection.MoveDown Unit:=wdLine, Count:=1
Selection.HomeKey Unit:=wdLine
Selection.EndKey Unit:=wdLine, Extend:=wdExtend
Selection.Copy
Selection.EscapeKey
ActiveDocument.Close
WordBasic.ViewFooterOnly
Selection.TypeText Text:="Document "
ActiveWindow.ActivePane.View.SeekView = wdSeekMainDocument
Else
MsgBox ("Failed to find cover page")
End If