The Parodies database page now shows a total of 240 parodies, mainly documented by (and taken from) the bibliography of the rubáiyát by A.G. Potter (1929), Jos Biegstraaten’s study ‘Omar with a smile’ (2004), Michelle Kaiserlian’s thesis Infinite Transformation (2010), Roger Paas’ catalog Edward FitzGerald’s Rubáiyát of Omar Khayyám and Related Materials (2023).
I recently discovered more than twenty parodies in online resources as HathiTrust Digital Library and Trove, a collaborative effort of organisations, communities and individuals in cooperation with the National Library of Australia. The number of quatrains varies from 1 to 27, published between 1902 and 1937, and they do not appear in the above mentioned sources.
In Trove I found a number of parodies in The Bulletin, whereas in the Hathi Trust Digital Library ten parodies appeared in Yale record, most of them dealing with various aspects of college life.