Would add that, when Eliza demands to see what Higgins has written, she remarks that she can't read it, as "that ain't proper writing, that ain't", which confirms that he would have been using IPA, or some variant of his own.

Also, re the indefinite vowel, in E Anglian dialect, even the final y, in standard English pronounced like ee, sometimes becomes the indefinite vowel: Harry Cox, of Catford, Norfolk, used for example to sing the line in The Shooting Of His Dear as "Off goes young Jimma with his dog and his gun" - though if asked to write it he would have written the name as 'Jimmy'.

~M~