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I don't know that I'd call the distillation method unimportant, but it's true that the mash is pretty key with English-style rums.
“English: The history of the English style took off with Britain finding Barbados, an island that was off of the major chain of islands and therefore had not been discovered or claimed by France or Spain. On Barbados, the English invented factory or modern production styles. One truism to this style is that the distillation methodology is unimportant with stills ranging from wooded ones to very formal and recognizable ones. What is important is the dunder; the mash is left in the fermenter and more molasses is added in. This style produces a resinous, rich style full of esters that allows it age well, be transported, and left on docks for storage. In Jamaica, they often take this to an extreme where they keep fermenting until the molasses mash stops bubbling, take some of it off for distillation, replenish the volume, and sometimes they never clean out the fermentation tank. The age statement on English rums is the minimum age.”