In the meantime, I figured out a solution to my question which works
quite nicely (with KeyBindings).  However, in going to check the settings
you referred to, I found that I could not get rid of my solution -
event explicitly clearing the KeyBindings.ClearAll and shutting down
Word was not sufficient.  I eventually had to remove the functions
that the KeyBindings hooked into, and when I replaced them, things
operated normally.

OK, first of all those settings were checked, and it was the
'Autoformat As You Type' tab that I had to uncheck to remove the
replacement of "Straight Quotes" with "Smart Quotes".  But the
fact is that I like Smart Quotes, except when I'm in a code
section.  Furthermore, I don't think I can gain the type of
functionality I'm after with AutoCorrect.

So here is the solution that I have.  It seems to be working
nicely, and I am so far quite pleased with it.  I put
the following code into a module within the document and have
to enable macros:
Tools \ Macros \ Security \ Trusted Publishers then set
Trust Access to Visual Basic Project
Also, to avoid getting asked each time I also had to select:
Tools \ Macros \ Security \ Security Level \ Low

Sub AutoOpen()
  Application.KeyBindings.ClearAll      'Spotty track record
  CustomizationContext = ThisDocument   'else goes to Normal.Dot
  KeyBindings.Add wdKeyCategoryMacro, "SQuote", wdKeySingleQuote
  KeyBindings.Add wdKeyCategoryMacro, "DQuote", _
                  BuildKeyCode(wdKeyShift, wdKeySingleQuote)
End Sub

Function rightSideTest(sel As Selection)
  'return true if sel follows a character after
  'which there should be a closing quote
  rightSideTest = sel.Start > 0
  If Not rightSideTest Then Exit Function
  ask = Asc(sel.Document.Range(sel.Start - 1, sel.Start).Text)
  If ask <= 27 Then
    rightSideTest = False
  ElseIf ask = Asc(" ") Then
    rightSideTest = False
  ElseIf ask = Asc("[") Then
    rightSideTest = False
  ElseIf ask = Asc("{") Then
    rightSideTest = False
  ElseIf ask = Asc("(") Then
    rightSideTest = False
  ElseIf ask = Asc("<") Then
    rightSideTest = False
  End If
End Function

Sub SQuote()
' Put in a right/left single quote except in Courier make it straight
  Dim newChar: newChar = "'"
  If Mid(Selection.Font.Name, 1, 7) <> "Courier" Then
    If rightSideTest(Selection) Then newChar = ChrW(8217) _
                                Else newChar = ChrW(8216)
  End If
  Selection.TypeText newChar
End Sub

Sub DQuote()
' Put in a right/left double quote except in Courier make it straight
  Dim newChar: newChar = """"
  If Mid(Selection.Font.Name, 1, 7) <> "Courier" Then
    If rightSideTest(Selection) Then newChar = ChrW(8221) _
                                Else newChar = ChrW(8220)
  End If
  Selection.TypeText newChar
End Sub

Csaba Gabor from Vienna