Finding same shapes without additional parameters

Hello, all! Another question has popped up.

I have received a file with a lot of shapes placed onto an area using a nesting program. Good part is they are placed efficiently, bad part is they do not have any data on them (rotation, names, IDs, etc). All the placed shapes are not rotated, only mirrored (well, rotated 180 degrees). The task is to place different content into the mirrored and non-mirrored shapes. And this is not a one-off thing so I decided to make a macro for it.

I made a sort-of select-same macro which would use Shape size, node counts and, in my mind, first node positions relative to their centers as parameters to find same shapes. And it works really well, apart from mirrored (rotated 180 degrees) shapes in the original. It selects both regular and mirrored shapes no matter what I try.

Here is the code:

Private Sub SelectSame()

    If ActiveDocument Is Nothing Then
        MsgBox "Please have a document open!", vbOKOnly Or vbExclamation, ""
        Exit Sub
    End If

    If ActiveSelectionRange.Shapes.Count = 0 Then
        MsgBox "Please have at least one selected shape!", vbOKOnly Or vbExclamation, ""
        Exit Sub
    End If

    Dim S As Shape, T As Shape
    Dim SR As New ShapeRange
    Dim A As Double, B As Double

    Set S = ActiveSelection.Shapes.First
    If S.Type <> cdrCurveShape Then
        MsgBox "Shapes need to be curved!", vbOKOnly Or vbExclamation, ""
        Exit Sub
    End If
    ActiveDocument.Unit = cdrMillimeter
    For Each T In ActivePage.FindShapes(, cdrCurveShape)
        If T.SizeHeight > (S.SizeHeight * 0.9999) And T.SizeHeight < (S.SizeHeight * 1.0001) Then
            If T.SizeWidth > (S.SizeWidth * 0.9999) And T.SizeWidth < (S.SizeWidth * 1.0001) Then
                If T.Curve.Nodes.Count = S.Curve.Nodes.Count Then
                    If Abs(T.Curve.Nodes.First.PositionX - T.CenterX) > Abs(S.Curve.Nodes.First.PositionX - S.CenterX) * 0.999 And _
                        Abs(T.Curve.Nodes.First.PositionX - T.CenterX) < Abs(S.Curve.Nodes.First.PositionX - S.CenterX) * 1.001 Then

                            SR.Add T
                    End If
                End If
            End If
        End If
    Next T
    If SR.Shapes.Count <> 0 Then
        SR.Shapes.All.ApplyUniformFill CreateRGBColor(255, 0, 0)
    End If
End Sub

Those 0.9999 numbers are to overcome CorelDRAW's (or general) floating point comparison limitations, I guess.

And to make testing easier here's an initial file I am using for testing (for some reason I could not directly place it here):

If any of you have some idea on how to efficiently select only the truly similar shapes, such as ((( and not ((( and ))), I would greatly appreciate it. One, seemingly inefficient option, would be to place (a copy of) the shape that needs to be compared on top of the sample shape and compare all the node coordinates. And if nothing else comes up I will probably use that. But perhaps the true pros here know of a better approach.

Thanks in advance!