The reason we sing 'Martinmas' instead of 'Michaelmas' is a cultural thing. Where we come from, a little further north than Mike, the hirings at Martinmas were the commencement of the early ploughing. The tradition of plough-lads dancing in the villages of East Yorkshire also occurred at this feast. (There's nothing in the song that's overtly regional apart from the title) We altered the word because it feels more 'comfortable'.
Thanks for singing it to such an appreciative crowd Sue, the song deserves all the support it can get.