This is where I can chime in. You're both right, actually. And you're both talking about very different stories.
You see, the genre a writer writes in matters - quite a lot. You would not see a Snerg getting all melancholy, wounded, and broken as Frodo is in LOTR. But you could see the Bilbo Baggins of "The Hobbit" as a lot closer to Gorbo and the Snergs - for the reasons you've cited above.
How can I put it . . . Hobbits changed since Tolkien first "discovered" them in the 1930s and when they ultimately entered LOTR. And actually, very early in the drafting process, the LOTR Hobbits become something very different. "Trotter" was a traumatized Hobbit who had apparently survived the torments of the Black Riders, who at that point were still just regular human thugs in black outfits riding out of a William Morris novel. Trotter ultimately became Aragorn. The trauma went to Frodo throughout his journey.
Now, yeah, Frodo's not a typical Hobbit in that way. Nor are Sam, Merry, or Pippin. And the Bilbo Baggins we encounter in the LOTR is this learned, older Hobbit who is basically copying-down what becomes "The Silmarillion"; he writes the two versions of "The Hobbit" within the frame of the tale.
And it's those two versions that show us the concept the most. Again, you're very right that Tolkien borrowed some of their appearances and love of food, and perhaps some of their adventurous hijinks, from the Snergs. But - - - that's in the early version of "The Hobbit" that's very separate from LOTR, where the Ring is just a magic ring that makes someone invisible without any malevolence, where Gollum is a friendly creature who doesn't try to eat Bilbo, and so on and so forth.
Tolkien actually tried to rewrite "The Hobbit" after he wrote LOTR. His publisher wouldn't let him. All they would allow for was a new edition that would have a newly written account of the Ring and Bilbo's finding of it. That was pretty much it. It's very clear to me, at least, that the more Tolkien wrote, and the more the LOTR became part of his legendarium and far less "a sequel to 'The Hobbit,'" and the more it became a more mature book for older readers - - - which Tolkien actively intended to do - - - the less his Hobbits resemble the Snergs and the more they resemble "rustic English folk."
When I read the lines of Frodo, Sam, Merry, and Pippin, they really don't strike me as otherwordly fairy tale creatures. They strike me as people - and as the most human, the most down-to-earth (*especially Sam) characters throughout the LOTR.
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Tl;DR: in short - - -> Hobbits evolved and changed in Tolkien's mind as he wrote them throughout the years. The more particular they became to Middle-earth, the more they departed from their early influences. Tolkien was very strong-minded about wanting to avoid conscious influences on his writing; it was simply his way. He strove for originality - and that's where I think he really wanted to iron things out the more time went on. What I do love about that quote you gave is that we catch him there admitting to an "unconscious influence" on his earlier work in "The Hobbit." Eureka!
So again, you're right: Wyke-Smith's tale has a strong influence on the original "Hobbit" and what Hobbits look like in it and how Bilbo's portrayed. Some of those elements stay appearance-wise. By the time we get to Frodo's departure into the Uttermost West, however, "we're not in Kansas anymore" - like how "Concerning Hobbits" at the start of LOTR really grounds them as a people, and of course, by the time we reach the ending of the LOTR, it's a different tale entirely
Cheers!