Michael Dirda has a level-headed review of recent Lovecraft books, in The Times Literary Supplement. Currently the article is free, though it may slip behind the TLS paywall in the future.

In the commentary on “The Shadow Over Innsmouth” [in Klinger’s Annotated], one looks in vain for any mention of Robert W. Chambers’s “The Harbour-Master” (part of In Search of the Unknown), the story from which Lovecraft borrowed a central element of his plot. In short, the knowledgeable Lovecraftian is likely to feel that Klinger has done admirable work, but could have probed more deeply.”

I think I have to agree with Klinger for omitting mention of this speculative and tenuous ‘source’. Lovecraft knew of the story from as early as 1927, indicated by his opening a letter to F.B. Long (6th July 1927) with…

Sir Harbour-Master:—”

In November 1928 Lovecraft wrote to Farnsworth Wright, of a friend’s proposed anthology…

I am suggesting that he use … Harbour-Master.”

In a letter to F.B. Long of 17th October 1930…

Speaking of literature … Little Augie Derleth [has shipped] me a gratuitous batch of his bibliothecal discards [including] Chamber’s In Search of the Unknown (God! The Harbour Master!!!)”

This latter was the re-written version of the story, for the anthology In Search of the Unknown (1904). In I Am Providence, Joshi implies this 1930 date was the date from which an influence on “Innsmouth” might be traced, which is congruent with the 1931 date for “Innsmouth”. But the earlier letters I note above suggest a prior date of summer 1927, and thus Lovecraft’s comment of “God! The Harbour Master!!!” does not necessarily imply that he had seized the book from Derleth’s box and had only just then finished reading the story. He may have simply been remembering his reading of it from circa 1927 or earlier.

In any case, there is no real evidence for direct influence on “Innsmouth” other than that: i) it was obviously well regarded by Lovecraft, and ii) the monster in “The Harbour-Master” is a sort of lone hybrid eel-man…

At that moment, to my amazement, I saw that the boat had stopped entirely, although the sail was full and the small pennant fluttered from the mast-head. Something, too, was tugging at the rudder, twisting and jerking it […] a sudden wave seemed to toss on deck and leave there, wet and flapping — a man with round, fixed, fishy eyes, and soft, slaty skin. But the horror of the thing were the two gills that swelled and relaxed spasmodically, emitting a rasping, purring sound — two gasping, blood-red gills, all fluted and scolloped and distended. […] The harbor-master had gathered himself into a wet lump, squatting motionless in the bows under the mast; his lidless eyes were phosphorescent, like the eyes of living codfish. […] the next I knew the harbor-master ran at me like a colossal rat […] his limbs seemed soft and boneless; he had no nails, no teeth, and he bounced and thumped and flapped and splashed like a fish, while I rained blows on him with the boat-hook that sounded like blows on a football. And all the while his gills were blowing out and frothing, and purring, and his lidless eyes looked into mine …”

But human-animal hybrids (centaurs, fauns, mermaids, werewolves etc) are not at all uncommon in weird literature, and there are scattered fish-men and frog-men to be found in folklore (a book from the era of Lovecraft’s youth, on the Indian folklore of Yosemite, led with a primal creation story of the Frog-man who helps Coyote-man to create the earth). So I think Klinger was probably right to omit a claim for “The Harbour-Master” as a source for “Innsmouth”. One might equally plausibly suggest that Lovecraft was inspired by the title of the Poe story “Hop-Frog” (1849), in which a deformed dwarf is forced by his physique to hop like a frog…

Hop-Frog could only get along by a sort of interjectional gait — something between a leap and a wriggle”

Nor were frog-men and similar hybrids absent in early weird fiction. What about the tiara-wearing frog-women and frog-men in Merritt’s book-length version of The Moon Pool (1919, reprinted Amazing Stories May-July 1927). A novel which we know that Lovecraft read, and disliked in favour of the original short story…

a gigantic frog — A WOMAN frog, head helmeted with carapace of shell around which a fillet of brilliant yellow jewels shone; enormous round eyes of blue circled with a broad iris of green; monstrous body of banded orange and white girdled with strand upon strand of the flashing yellow gems; six feet high if an inch, and with one webbed paw of its short, powerfully muscled forelegs resting upon the white shoulder of the golden-eyed girl! […] The gigantic eyes of the frog-woman took us all in — unwinkingly. Little glints of phosphorescence shone out within the metallic green of the outer iris ring. She stood upright, her great legs bowed; the monstrous slit of a mouth slightly open, revealing a row of white teeth sharp and pointed as lancets; the paw resting on the girl’s shoulder, half covering its silken surface, and from its five webbed digits long yellow claws of polished horn glistened against the delicate texture of the flesh.”

And through the portal marched, two by two, incredible, nightmare figures — frog-men, giants, taller by nearly a yard than even tall O’Keefe! Their enormous saucer eyes were irised by wide bands of green-flecked red, in which the phosphorescence flickered. Their long muzzles, lips half open in monstrous grin, held rows of glistening, slender, lancet sharp fangs. Over the glaring eyes arose a horny helmet, a carapace of black and orange scales, studded with foot-long lance-headed horns. […] The webbed hands and feet ended in yellow, spade-shaped claws. […] And then, quietly, through their ranks came — a girl! Behind her, enormous pouch at his throat swelling in and out menacingly, in one paw a treelike, spike-studded mace, a frog-man, huger than any of the others, guarding. But of him I caught but a fleeting, involuntary impression — all my gaze was for her.”

Or Victor Rousseau’s “The Sea-Demons” (All-Story, January 1916) in which invisible sea creatures living off the Shetland Islands, with a hive mind, plan to invade the land.