Boffer - I need to ask your source for it being the Duchess of Teck's collet necklace - because I have now looked more closely at all the drops. I put the following proposition as a reworking of Queen Victoria's diamond necklace and earrings:
From the two bows, the lower drop would be Cullinan III and the higher drop the Lahore diamond, from Queen Victoria's necklace, or coronation necklace as now known. I say the Lahore because there is no Cullinan of that shape.
The drops from the cockade sides could be two-thirds of Queen Victoria's earrings. Queen Mary's earrings might be the top third? Queen Mary did not seem to ever wear long drop earrings. Edit: For her own coronation she did not wear the drop earrings.
So the long necklace could be Queen Victoria's extended. I came back to this idea because of the sudden change in size of the diamonds.