None of us had much faith that it could be fixed, but it was determined that I couldn't make it any worse as it wasn't wearable as it was. So I took it home and took it apart and gave all the pieces a good pressing with a bit of steam.
You can see the difference here between the thin end, which has been ironed, and the wide end, which is yet to be pressed.
I pinned and hand-stitched the thing back together and the tie made a suprisingly full recovery. MM was most chuffed.