Why do we rattle noisemakers at the mention of Haman's name?

Another old post; last one I promise.

Why do we rattle noisemakers at the mention of Haman's name?

There's a temptation to link the practice of noise making in the synagogue to the verse 'Thou shalt blot out the remembrance of Amalek' (Deut. xxv. 19)' but I've found no evidence that this custom existed prior to the middle ages.

Most everything you can find using Google, will agree with Wikipedia which attributes the custom to:

French and German rabbis of the thirteenth century who introduced the custom of writing the name of Haman, the offspring of Amalek, on two smooth stones and of knocking or rubbing them constantly until the name was blotted out. Ultimately, however, the stones fell into disuse, the knocking alone remaining. Some wrote the name of Haman on the soles of their shoes, and at the mention of the name stamped with their feet as a sign of contempt; others used for the same purpose a rattle--called 'gregar' (from Polish grzgarz), and producing much noise--a custom which is still observed by the Russo-Polish Jews.

Interesting, but our familiar problem remains. How was the custom established? What brought it into being? Did the French and German rabbis of the thirteenth century meet at an Aguda convention, where they resolved that a new custom was needed? If so, where is the record of their proclamation? Did they vote? Was there debate? Were other ideas considered?

Or were the Rabbis of medieval Europe simply as promiscuous about introducing new customs as our modern Rabbis are about issuing bans?

Analogues [Sources and other material]
Our question ("How was this custom brought into being?") becomes stronger when you consider two non-Jewish practices. Of course, neither analogue comes with a signed note asserting that it is the official antecedent of our Purim custom; still they are interesting.

In Jewish Festivals A Guide to Their History and Observance, Hayyim Schauss maintains (page 265) that ancient people thought themselves vulnerable to the influence of evil spirits and would often made loud noises for the purpose of driving the spirits away. Haman, you will remember, was the name of the Persian underworld demon. Possibly, driving away the demon at springtime was a pagan rite the Jews borrowed.

Another idea, cited by Tzidkuni, suggests the custom has a direct Christian antecedent. He writes that on the first night of Passover, Christian children would go through the streets of Jewish neighborhoods and congregate around the synagogues with noisemakers to eradicate the memory of Judas Iscariot. On that night, the priests would also 'eradicate the memory' of Judas with great noisemakers or by pounding sticks upon wooden boards suspended from the Church steeples.

Is it a coincidence that Jews, Christians and pagans all had a spring noise rite connected to the eradication of a despised character? Perhaps. Is there a firm link between the three customs? No. But this blog was not created to promote certainty. This blog was created (in part) to throw sand in the eyes of people who insist that everything Jews do today was known to Moshe and his Sanhedrin (bearing in mind, of course, that Sanhedrin is a Greek loan word, making it unlikely that Moshe had anything of the sort. See? I did it again.)