Sorry it's taken so long to get back to you all
Carpenter noted that

"it was widely sung in Barbados.
And that a burton is a term used for a block & tackle
used in hoisting, particularly among longshoremen.

A burton is certainly a single block & tackle which could be doubled or tripled to take a heavier load.
The main old harbour in Barbados, Bridgetown, is lined with warehouses now all trendy wine-bars & posh boutiques.

As to 'Booch free'
I have it on good authority that the 'booge' of a barrel is the widest part.
And that when the 'booge is free' that the bunge is easy to get to and the barrels aren't touching each other.

Another possible explanation for 'burtoned in the archway'
If a cask is stored athwartships (port to starboard not bow to stern!) it is said to be "a-burton"
It's not clear if the barrel was to be standing or lying for this position though.

Hope this has been helpful to anyone who might be interested!