The "divers for crotchets" phrase appears not only in Poe's Eureka:
And now, before proceeding to our subject proper, let me beg the reader’s attention to an extract or two from a somewhat remarkable letter, which appears to have been found corked in a bottle and floating on the Mare Tenebrarum—an ocean well described by the Nubian geographer, Ptolemy Hephestion, but little frequented in modern days unless by the Transcendentalists and some other divers for crotchets. The date of this letter, I confess, surprises me even more particularly than its contents; for it seems to have been written in the year two thousand eight hundred and forty-eight. As for the passages I am about to transcribe, they, I fancy, will speak for themselves.
but also his Mellonta Tauta:
I have the honor of sending you, for your magazine, an article which I hope you will be able to comprehend rather more distinctly than I do myself. It is a translation, by my friend, Martin Van Buren Mavis, (sometimes called the “Poughkeepsie Seer”) of an odd-looking MS. which I found, about a year ago, tightly corked up in a jug floating in the Mare Tenebrarum—a sea well described by the Nubian geographer, but seldom visited now-a-days, except for the transcendentalists and divers for crotchets.
Kent Ljungquist discusses the identity of the Nubian Geographer and suggests a link to Poe's "A Descent into the Maelström". Ljungquist indicates that Poe's knowledge of the Nubian Geographer originated in Jacob Bryant's book A New System, or, an Analysis of Ancient Mythology.
Bryant (v. 3, pp. 59-60), writing about the Titans' being consigned to the dark, says:
The vast unfathomable abyss, spoken of by the poets, is the great Atlantic Ocean; upon the borders of which Homer places the gloomy mansions, where the Titans resided. The ancients had a notion, that the earth was a widely-extended plain; which terminated abruptly, in a vast cliff of immeasurable descent. At the bottom was a chaotic pool, or ocean; which was so far sunk beneath the confines of the world, that, to express the depth and distance, they imagined, an anvil of iron tossed from the top would not reach it under ten days.
Also (v. 3, p. 60):
To this Atlantic region the Titans were banished; and supposed to live in a state of darkness beyond the limits of the known world.
Finally (v. 3, p. 61):
By the Nubian Geographer the Atlantic is uniformly called according to the present version Mare Tenebrarum.  Aggressi sunt mare tenebrarum, quid in eo esset, exploraturi. They ventured into the sea of darkness, in order to explore what it might contain.
 Geog. Nubiensis. p. 4. p. 6. and p. 156.
From Bryant, we see that the Mare Tenebrarum is the deep, dark, abyss of the Atlantic Ocean, whose bottom is so far down that its characteristics are unknowable.
To tie this to the Poe quote, the meaning of crotchet that seems to be most relevant is "an odd fancy of whimsical notion", or even "a perverse notion" (dictionary.com).
Being that the ocean is metaphorically so deep that it would take an anvil ten days to reach the bottom, it would be folly to attempt to explore it by diving. Thus only those possessed of a perverse or whimsical notion would do so.
To further support and expand this theory, I have found an analysis of this work by Charles W. Schaefer (pp. 357-358):
Among the ways here satirized is New England Transcendentalism, which is the object of repeated mockery. The Transcendentalists, says Poe,
are frequenters of the Mare Tenebrarum where they dive for crotchets. They are, further, descendants of Kant, who first proposed the ideas of
Transcendentalism, and in his memory have made his ideas their cant.
. . . .
[I]t is interesting from the standpoint of Poe's aesthetics to note exactly what peculiarities of Transcendentalism come under his criticism. First,
he alleges, they frequent dark waters in order that they might dive for crotchets (whims, fancies, and perhaps novelties). Second, they are the
followers of Kant, who, as a devoted disciple of Aristotle-especially Aristotle's a priori system-vindicated intuition in his Critique of Practical
From Poe's standpoint, to believe that transcendent truths are recognizable only by means of a transcendent faculty—as Kant and the New England
Transcendentalists believed—is to endanger the proper concept of art, mistaking for art anything that is dark (Tenebrarum), whimsical and
novel (crotchets), and supposedly deep (Mare).
One could take this much deeper, and people have. I recommend that you follow up the references if you want a full scholarly analysis. Bryant is available at the Internet Archive, and Ljungquist and Schaefer are available from JSTOR.
- Bryant, J. (1774). A new system; or, An analysis of ancient mythology: Wherein an attempt is made to divest tradition of fable; and to reduce the truth to its original purity .. London: Printed for T. Payne, P. Elmsly, B. White, J. Walter.
- Ljungquist, K. (1976). Poe's Nubian Geographer. American Literature, 48(1), 73-75. doi: 10.2307/2925315
- Schaefer, C. W. (1971). Poe's "Eureka:" The Macrocosmic Analogue. The Journal of Aesthetics and Art Criticism, 29(3), 353-365. doi:10.2307/428978