Since Taylor was president of the US in 1850 and was a slave holder from Baton Rouge (just up river from New Orleans) the assumption that sailors in the Gulf Ports hadnt heard of him holds no ice with me.
Just because he has almost vanished into obscurity nowadays doesnt mean he wasnt a legend when this shanty first came to notice.
So why do you think there were two versions, one pro and the other anti?
The coloured workers would have been more likely to sing the pro version, surely? Certainly within earshot of their white 'masters' at any rate. At sea it would be a diferent story, especially when among non-Yankee sailors.