Is cosmic horror still frightening to a modern audience? Let us first define cosmic horror. In a nutshell, cosmic horror is about the insignificance of humanity and our powerlessness in the face of a cold indifferent universe. The horror in a Lovecraft story mainly comes from people learning some facet of the true nature of the universe combined with their inability to make any meaningful changes in broad scheme of things. This is a fairly abstract fear and I don’t think it would work on most people in 1932 never mind in 2019. But that doesn’t mean cosmic horror can’t be used effectively...Cosmic horror can be effective but it's got to threaten things the player character cares about. It's got to threaten their families, their sense of identity, their faith in the pillars of society, etc., etc. The cosmic horror comes when the things the players care about are either destroyed or his faith in them are destroyed.
Ok, that's seems like a self-evident observation, but to put it plainly like that is clarifying and like many observations that are self-evident when you hear them being able to state them with clarity requires more understanding than one might think.
Yes, the reason cosmic horror was deeply effecting to HPL is that discoveries in math and science undermined his faith in things he cared deeply enough about that they defined his identity. His beliefs were shook. So it stands to reason that concepts like "insignificance of humanity and our powerlessness in the face of a cold indifferent universe" will only be horrifying if they can be made to intersect something that someone in 2019 deeply cares about. I would also suggest that the power of horror is to make you do more than reflect upon something you know to be true (or hope is not true), but to actually feel it. In other words, you have to not only know about the heat death of the universe, but feel that in some way this is real and impacts on you - the difference between mere intellectual affirmation and actual belief. Horror makes you not only know that being alone in the dark with unidentifiable noises can be scary, but actually feel that fear. That I think is the hard part in trying to obtain the result of horror in game. You have to someone trigger a deeper introspection than normally happens in a game.
I would suggest that the same sort of cosmic horror that HPL felt could be visited on people from 1932 or 2018, but it is very hard to get people to introspect deeply on the sort of things that trigger that horror. Most people are, like the characters on the edge of an HPL, quite happy to ignore all the evidences of their senses and their intellect if in doing so it will prevent them from contemplating something that horrifies them. In Charles Stross's laundry files, Stross voices what I think is a very Lovecraftian sentiment through the voice of his protagonist Bob, when Bob stats that he would prefer to live in a universe without gods, but the reality of a true religion has been forced on him quite against his will because he knows he lives in a universe with deities, and it is horrifying. Likewise, to pick up some communities that I hope do not have too many members here (and if anyone feels attacked, I assure you I'm more sympathetic than you might imagine and please IM me about it), a Flat Earther or someone convinced that the universe is 4000 years old, or someone convinced that the moon landing was a hoax, is I think doing quite a good job of blocking out thoughts that horrify them and would be quite as troubled as HPL was by the Big Bang. Again, if anyone feels assaulted by that, I assure you I think such behavior is human behavior and not a sign of uncommon mental or social defect, as someone as bright as Einstein is asserting very much the same horror in a statement like, "God does not play dice with the universe." As much horror as quantum dynamics had for Einstein, imagine how much worse it would have been had Einstein been forced to confront evidence that the 'god' in that statement was not a metaphorical or pantheistic impersonal summation of the laws of the physical universe, but the sort of personified being that Bob is forced to accede the reality of in the Laundry-verse.
Picking on Stross, one aspect of the Laundry verse that I think ruins the horror is one that I felt ruined the horror in my attempt at a CoC campaign, and that is the sense that an RPG tends to give that the protagonists have some measure of control. The horror of the laundry-verse has for me been continually diminishing as the protagonists in the setting 'level up' to increasing degrees of (to use the technical term) "badassery". Whereas in the CoC setting one would expect that as you learn more mythos lore, and in particular as you become more of a Lovecraftian sorcerer, one would get more and more unstable and monstrous until ones humanity is stripped away. But in the Laundry-verse, this hasn't been happening as Stross moves away in the story from contemplating the things that horrify him. Rather, as the story continues Bob is more or less friends with a variety of Lovecraftian horrors and gets more and more in control and less and less in danger as the story goes on. Indeed, lately Stross has been less contemplating the horror of being forced to contemplate a theistic universe that he doesn't want to exist that we see in 'Colder War' or 'The Atrocity Archives', than he has been contemplating how cool it would be to live in a universe where he could be a superhero that could punch Dread Cthulhu in the face. Consider the difference between what you related regarding the story of "Shadow over Innsmouth", and the way Deep Ones have been treated in recent Laundry verse stories as being friendly sexy superheroes rather less alien or frightening than J'onn J'onzz. "Shadow over Innsmouth" ends with the cosmic horror of evolving into something horrifying in form and mind. The Laundry verse is increasingly about humanity leveling up, as if Lovecraftian transformation was something to be welcomed and not feared.
Which has prompted me to say several times that the Laundry files are from a Lovecraftian perspective, most horrifying viewed from the meta perspective.
This is similar to the idea "Wouldn't it be cool to live in the universe of Pacific Rim?" suggested by the idea that if Kaiju were real, well then giant battling robots would be real too and so in that sense it might be desirable to live in a universe with giant rampaging monsters. "May you live in interesting times" seems to have lost its power to terrify. The deep sense of cosmic horror people once felt about ideas like nuclear war seems to have largely faded away. That horror has become abstract as well, and in that sense I think you are probably wrong about the relative portion of people who could be horrified by abstract ideas like the inability of mankind to save themselves from destruction comparing 1932 and 2019. Bring up the extinction of humanity these days, and there is a not insignificant portion of the audience that avows that would be a good thing.
So what are the things which a modern audience is going to be actually threatened by? What horrifies the modern reader? Sure the insolvability of Diophantine sets is an abstract thing, but underlying it is a profound weirdness that attacks deeply held intuitive convictions many people have, which might be described as the conviction that there is a solution within the grasp of humanity for every problem. But, supposing it is too much to write an adventure that conveys that connection, what can you write an adventure about that actually stops a modern player in his tracks and makes him go, "Woah." You mention the body horror of The Fly, and I think of the rather well received Delta Green adventure Convergence (?, I think I have that name right). But too much body horror is not only repetitive it tends to end up in just squick, with vomit and the like provoking disgust and squeamishness rather than intellectual horror. So where else can we go to threaten the basic beliefs of someone in 2019 and force them to think of things that they'd rather not think of (well, at least in some sense, since obviously the whole point in a horror game or movie is to make you think things you'd rather not think for the visceral thrill and frisson of doing so).