"As per previous thread, the public consensus is that it would be near impossible to craft something better than Teeming Necklace
Hence, my challenge is to prove them wrong."
Hmm, how can you prove them wrong?
As I understand it, you are going to try to craft something better?
Even if you got something better in the first try, it would not mean anything,
Only way to prove them wrong would be to get the actual % chance of getting something better, and that actual chance would be shown to be quite high. That way it will turn out that everyone has just been unlucky lol.