Vertex as x,y co-ordinates from face center for animated object

Question

I'm trying to obtain the selected face vertex locations for an animated Object as x,y co-ordinates relative to f.calc_center_median() as the origin center [0,0] (assuming a planar face). The way I've approached it at the moment is by moving the origin point to the face center and rotating according to the face, but I'm running into a number of issues...

1. The vertex locations are still coming through as local, even when multiplied with the matrix world?
2. Non-uniform scale messes up the face rotation matrix (tried to avoid this by applying the bmesh but that also messes the rotation matrix)
3. For an 'even edged' face (eg. a cube face) I can't work out how to avoid the x,y rotation from flipping randomly over the duration of the animation?

Any suggestions on fixes, or alternative ways to approach this? This is what I have so far (in the final function I don't want the object to actually move, just moving for testing)...

import bpy
import bmesh
import mathutils
ob = bpy.context.edit_object
frame_start = bpy.context.scene.frame_start
frame_end = bpy.context.scene.frame_end
ob_faces = {}
for fr in range(frame_start,frame_end):
    bpy.context.scene.frame_set(fr)
mw = ob.matrix_world
me = ob.data
bm = bmesh.new()
dg = bpy.context.evaluated_depsgraph_get()
bm.from_object(ob, dg)
bm.transform(mw)
bm.normal_update()
# bm = bmesh.from_edit_mesh(me)

selverts = [v.co for v in bm.verts if v.select]
if len(selverts):
    pt = sum(selverts, mathutils.Vector()) / len(selverts)
    #T = Matrix.Translation(-pt)
    bmesh.ops.translate(bm, vec=-pt, verts=bm.verts)
    # mw.translation = mw @ pt
    mw.translation = [0,0,0]

for f in bm.faces:
    if not f.select:
        continue

    n = f.normal
    t = f.calc_tangent_edge_pair().normalized()
    bt = n.cross(t).normalized()
    M = mathutils.Matrix([t, bt, n]).transposed().to_4x4()
    M.translation = f.calc_center_median()

    ob.rotation_euler = M.inverted().to_euler()
    bmesh.update_edit_mesh(me)

    new_w = ob.matrix_world

    for v in f.verts:
        key = "face_" + str(f.index)
        print (mw @ v.co)
        ob_faces[key] = ob_faces.get(key, []) + [new_w @ v.co]
        # ob_faces[key].append(mw @ v.co)


print("\n", ob_faces)