I repeat my suggestion that the coordinators refer to recognized sources for the accepted spellings in both English and Swahili for these Muslim festival days.
Here is what I find from one source, Kiswahili Kwa Kitendo (1993), written by Sharifa Zawawi, a native of Zanizabar. She is/was a Professor Emeritus of Classical Languages. She taught Linguistics, Arabic, Swahili and Middle Eastern Languages and Cultures at The City College of the City University of New York (CUNY), Columbia University and the New York University. She writes: ...Waislamu ... Sikukuu yao ni 'Idd el-Fitr', yaani 'Idi Ndogo'. Siku hii inasherehekewa baada ya watu kufunga mwezi wa Ramadhani ... Sikukuu ya Waislamu ya pili ni 'Idd el-Hajj' au 'Idi Kubwa'. Hii ni Sikukuu ya mfungo tatu, siku ya kumi ya mwezi huo, yaani baada ya watu kuhiji Makka. Siku hii watu huchinja kondoo au mbuzi kutoa sadaka, na nyama huliwa na jamaa, na majirani...
Source: Sharifa Zawawi, Kiswahili Kwa Kitendo (Vol. 1), Africa World Press, Inc., 1993 (2nd reprint), p. 77.
One final thought: If there are no standard spellings for these festivals in English or Swahili, then Duo Swahili should definitely stop pretending that there are.