Is that (barelee) or (bareleye)?
I seem to remember Whall having something to say on this but I might be wrong. This affectation is not just in sea shanties though. You can see it in 19th century folksong when it occurs at the end of a line as a rhyme. I'm sure I've seen other threads on this.

Wreck of the Industry c1810
'We want no help,' again he cried
I'd thank you to move immediately(e)

Me messmates drowned and so must I
And down he went immediately(e)

Poor doggerel admittedly but it makes the point.
And that's how I sing it.

'So earleye in the morning crops up in lots of 19thc songs. It is so widespread that it is difficult to conceive of it only being a 20thc invention.