Jay,

Is something like this what you had in mind by method 3?

Sub Test()
Dim oString As String
oString = ActiveDocument.Range.Text
Dim i As Long
Dim j As Long
i = 1
While InStr(i, oString, "now") <> 0
 i = InStr(i, oString, "now") + 1
 j = j + 1
Wend
MsgBox j
End Sub

Public Sub ResetSearch()
With Selection.Find
  .ClearFormatting
  .Replacement.ClearFormatting
  .Text = ""
  .Replacement.Text = ""
  .Forward = True
  .Wrap = wdFindContinue
  .Format = False
  .MatchCase = False
  .MatchWholeWord = False
  .MatchWildcards = False
  .MatchSoundsLike = False
  .MatchAllWordForms = False
  .Execute
End With
End Sub

I like Helmut's approach - almost.

Unconventional is one thing but, first, it seems to rely on a bug. Not that
Microsoft would ever fix it. Second, the user has to see dialogs popping up
each time (apparently even if you hide the application). This can be fixed
by using the .Execute method. However, that does not return an error
(Err.Number = 0) so there is no string to parse and I'm back to the original
problem.

For completeness, here's some code to make it run automatically. Helmut did
the clever work, I added the SendKeys.

Sub test()
   Dim ss As String ' short string, the number of replacements
   Dim sl As String ' long string, the error message
   Dim l As Long    ' just a loop variable
   Dim oDlg As Dialog

   ActiveDocument.Range(0, 0).Select
   Selection.ExtendMode = False
   'ResetSearch

   Set oDlg = Dialogs(wdDialogEditReplace)
   On Error Resume Next
   oDlg.Find = "a"
   oDlg.Replace = "X"
   oDlg.ReplaceAll = True
   SendKeys "%a" 'This also relys on this dialog not changing in a
subsequent release.
   SendKeys "{tab}"
   SendKeys "{tab}"
   SendKeys "{tab}"
   SendKeys "{enter}"
   oDlg.Display
   'oDlg.Execute
   sl = Err.Description
   ' in localized versions you don't know
   ' where the number of replacements occurs in the text
   For l = 1 To Len(sl)
       If IsNumeric(Mid(sl, l, 1)) Then
       ss = ss & Mid(sl, l, 1)
       End If
   Next
   ActiveDocument.Undo
   'ResetSearch
   MsgBox " Found: " & ss & " times"
End Su

One thing I couldn't manage,
was to put the find-string in the message, like:

Helmut, using Ricado's adaption we can set a string value equal to
oDlg.Find and then:

Sub test()
Dim ss As String ' short string, the number of replacements
Dim sl As String ' long string, the error message
Dim l As Long    ' just a loop variable
Dim oDlg As Dialog
Dim oString As String
ResetFRParameters
ActiveDocument.Range(0, 0).Select
Selection.ExtendMode = False
Set oDlg = Dialogs(wdDialogEditReplace)
On Error Resume Next
oDlg.Find = "a"
oDlg.Replace = "a"
oString = oDlg.Find
oDlg.ReplaceAll = True
SendKeys "%m"
SendKeys "%y"
SendKeys "%a"
SendKeys "{tab}"
SendKeys "{tab}"
SendKeys "{tab}"
SendKeys "{enter}"
oDlg.Display
sl = Err.Description
For l = 1 To Len(sl)
 If IsNumeric(Mid(sl, l, 1)) Then
   ss = ss & Mid(sl, l, 1)
 End If
Next
ResetFRParameters
MsgBox oString & ": was found (" & ss & ") times"
End Sub

Sub ResetFRParameters()
With Selection.Find
 .ClearFormatting
 .Replacement.ClearFormatting
 .Text = ""
 .Replacement.Text = ""
 .Forward = True
 .Wrap = wdFindContinue
 .Format = False
 .MatchCase = False
 .MatchWholeWord = False
 .MatchWildcards = False
 .MatchSoundsLike = False
 .MatchAllWordForms = False
 .Execute
End With
End Sub

Yes.