I'm not sure of your 'flush out my custom styles' statement but you are trying to use a sledgehammer to crack an egg by stepping through a paragraph at a time. It is no surprise that you are missing graphics because you only select inline shapes and then further restrict those to one specific type.
I would prep the source file by applying 'Normal' style to the entire content and removing character and paragraph local formatting and then pasting that cleaned content across into the target document.
Code:
Sub CopyPasteToTemplate()
Dim InputDoc As Word.Document, OutputDoc As Word.Document
Set InputDoc = ActiveDocument
Set OutputDoc = Documents.Add 'Normal template by default
With InputDoc.Range
.Style = wdStyleNormal
.ParagraphFormat.Reset
.Font.Reset
OutputDoc.Range.FormattedText = .FormattedText
End With
OutputDoc.Activate
End Sub