I think Leadfingers has the answer - learning songs from other peoples recordings and NOT trying to get away from that particular delivery .
Over here, on the other side of the world, singers are inclined to sing songs the way they heard them.
So if you picked up a song from a Joan Baez record, you sang it that way but if it was from the Pogues, that's how it will come out.
You can hear the influences and the sources, singers or countries.
We not only have American sounding singers but Scots, mock Irish, Cockney and broad West country sounds turning up here.
But in our pub session, the rest of the punters just love something they recognise. And it has to have the 'right' accent, not a Kiwi one!
Robyn