I can't help directly with Steve Baggish's query, but I found some very interesting information on songs and poetry based upon "Chad Gadya", and links to further information at: https://www.jewishfolksongs.com/en/one-only-kid#poetry

The same site also has a page about the many cumulative songs found in various countries of Europe which bear a strong resemblence to Chad Gadya. https://www.jewishfolksongs.com/en/chad-gadya-related-folksongs