In New York at this time the National Republicans , or "Adams men," were a very feeble organization, and shrewd political leaders at once determined to utilize the strong anti-Masonic feeling in creating a new and vigorous party to oppose the rising Jacksonian Democracy. In this effort they were aided by the fact that Andrew Jackson was a high-ranking Mason and frequently spoke in praise of the Order. The alleged remark of political organizer Thurlow Weed , that a corpse found floating in the Niagara River was "a good enough Morgan" till after the election, summarized the value of the crime for the opponents of Jackson. In the elections of 1828 the new party proved unexpectedly strong, and after this year it practically superseded the National Republican party in New York. In 1829 it broadened its issues base when it became a champion of internal improvements and of the protective tariff. The party published 35 weekly newspapers in New York. Soon one became preeminent, the Albany Journal, edited by Thurlow Weed . The newspapers reveled in partisanship. One brief Albany Journal paragraph on Martin Van Buren included the words "dangerous," "demagogue," "corrupt," "degrade," "pervert," "prostitute," "debauch" and "cursed."
It means that the corpse was good enough to identify as Morgan, whether it was really Morgan or not. Identifying a corpse, any corpse, as Mr. Morgan, a Freemason from New York who went missing at that time, was a good way to stir up the idea being spoken of at the time, that Morgan's mysterious disappearance was the result of his being murdered for having divulged the secrets of the Masons. True or not, it was a good enough excuse to get the people riled up against the Masons, of which Jackson was one. After the election, the possible revelation that the corpse was not really Morgan would make no difference; the damage to Jackson would already have been done.

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I heard it in The Confidence Man also.

"If I am, it is less from the remembrance of their stratagems as to our stock, than from the persuasion that these same destroyers of confidence, and gloomy philosophers of the stock-market, though false in themselves, are yet true types of most destroyers of confidence and gloomy philosophers, the world over. Fellows who, whether in stocks, politics, bread-stuffs, morals, metaphysics, religion-be it what it may-trump up their black panics in the naturally-quiet brightness, solely with a view to some sort of covert advantage. That corpse of calamity which the gloomy philosopher parades, is but his Good-Enough-Morgan."

Melville lived at about the same time as Jackson, so he has taken a contemporary event which his readers would have known about, and used it as a label for a general category of phenomena which he is talking about in this paragraph. "with a view to some sort of covert advantage" is the text that shows the connection between the two, as does the use of the word "corpse".

This usage "his Good-Enough-Morgan" is not really different (in terms of linguistic machinery) from when we speak today of a head of a failed corporation as "having met his Waterloo". "Waterloo" no longer has the same literal meaning in such a context as it had when Napoleon was defeated at Waterloo.
While the Waterloo expression is still known today, the expression Good-Enough-Morgan leaves today's readers with a blank expression on their faces. Nevertheless, the linguistic phenomenon is the same in both cases. I believe that such word associations are called "metonymy".