Always trying to outdo ourselves. :)
The following code corrects an error in my initial logic and is also far faster and shorter:

Public Function MakeNewString(ByVal InputString As String) As String

InputString = Trim(InputString)
Do While InStr(InputString, Chr$(34))
InputString = Left$(InputString, (InStr(InputString, Chr$(34)) - 1)) & Chr$(39) & Chr$(39) & Right$(InputString, Len(InputString) - InStr(InputString, Chr$(34)))
Loop
MakeNewString = InputString

End Function