One way of getting round the man-sings-woman's-song dilemma is a slight bit of editing at the beginning, so that 'I am', e.g., becomes 'it's of'...

To clarify: take as an example On Board The Victory. The beginning,   'I am an unfortunate lady, My sorrows they are great, My tongue is scarcely able'...

would become, 'It is of an unfortunate lady, Her sorrows they were great, (She said) "my tongue is scarcely able"'... And go on from there --

This is an adaptation of many songs - e.g. The Month Of January, Banks Of Sweet Primroses, &c, which are already in the form of a narrator of indeterminate sex who meets a young woman & reports on what he hears her saying/singing. I think some such adaptation might already have happened at some point in the song's evolution.


See what I mean?