The least exotic theory of all, but almost certainly the true clue, traces "hunky-dory" to the archaic American slang word "hunk," meaning "safe," from the Dutch word "honk," meaning "goal," or "home" in a game.
To achieve "hunk" or "hunky" in a child's game was to make it "home" and win the game.
The question of where the "dory" came from brings us back to our old friend "O. K." -- they say "okey-dokey," thus engaging in what linguists call "reduplication," or the emphatic, joking repetition of parts of a word.
"Hunky- dory" is almost certainly a similar product of reduplication by children who had won their game.
Nice research but I dispute the logic of the article.
It may be that hunky-dory was the result of a bilingual pun, perhaps invented because American sailors knew the word dori and prefixed it with hunky as an imagined Japanese street of earthly delights. honc "place of refuge, hiding place." A theory from 1876, however, traces it to Honcho dori, said to be a street in Yokohama, Japan, where sailors went for diversions of the sort sailors enjoy. Air - "Limerick Races" One of the boys am I, That always am in clover; With spirits light and high, 'Tis well I'm known all over.
I myself frequently do this sort of neologizing word play. That citation does at least suggest that 'hunky-dory' was in common enough use in 1866 for the author not to see fit to explain its meaning, although it's a pity 'hefty' and 'kindy dusty' weren't explained as these have now disappeared from the language.
Edit: and I see below that hunky dory was used in a poem .. It seems that The Galaxy writer had been perplexed by the recent popularity of the the expression, which appears in several publications in 1866; for example, Google translates "non compos" as "not in control" but its translation of the full expression leaves much to the imagination: "Dover hook on the uptake." Origin in post-Civil War time seems to be realistic.