Hi Brock,
Using your code, I am only able to replicate the problem you describe if source document has its Section breaks. In such cases, you might choose to delete those Section breaks or change their formatting to 'same as previous'. As an example of the latter:
Code:
Sub Demo()
Dim myName As String, RngTmp As Range, Sctn As Section, HdFt As HeaderFooter
ChDir ActiveDocument.Path
myName = Dir("03*.doc*")
While myName <> ""
With Selection
Set RngTmp = .Range
With RngTmp
.Start = .Start - 1
.End = .End + 1
End With
.InsertBreak Type:=wdSectionBreakNextPage
.InsertFile FileName:="myName", ConfirmConversions:=False
.InsertBreak Type:=wdSectionBreakNextPage
With RngTmp
For Each Sctn In .Sections
With Sctn
For Each HdFt In .Headers
HdFt.LinkToPrevious = True
Next HdFt
For Each HdFt In .Footers
HdFt.LinkToPrevious = True
Next HdFt
End With
Next Sctn
End With
End With
myName = Dir()
Wend
Set RngTmp = Nothing
End Sub