Shake with ice, strain into a tall glass, and fill with crushed ice; alternatively, swizzling in crushed ice would not be out of place here. Garnish with freshly grated nutmeg.
In thinking about lesser known Tiki drinks that have stood the test of time in my mind, the Pago Pago from the 1940 The How And When came to mind. I thought about how it could be riffed into a Batavia Arrack drink, but it needed more changes to differentiate it from the original. One of the Batavia Arrack recipes that popped into my head was the more recent Seven Seas Swizzle that paired the spirit with green tea syrup, lime, and orange bitters. In researching the South Pacific, I came across a New England link in the Marshall Island chain. In 1823, the Nantucket-based whaler The Globe suffered a mutiny that led their ship to the Mili Atoll; the mutineers killed the captain and three officers, and they left the rest on the atoll where the natives did in all but two.