Actually Neonivek, there are plenty of examples of going toe-to-toe with the Elder Things in some Lovecraft stories. Do they outnumber the ones where the main character is shitting themselves in terror and running away? No. But the precedent is certainly there.
The Dunwich Horror immediately comes to mind. Though the narrator is not physically present at the incident, it's related how Armitage and a few others go up against something coming through the gateway on top of the mountain, and they literally force it back with nothing but sorcerous knowledge. In Whisperer In the Darkness, the secondary character and his dogs go to town on a bunch of insectoid star travelers for weeks.
That's the Catch 22 in CoC games, magic. Is it enough to stop an Elder God? Absolutely not. But it's more affective against Elder Things than any mundane weaponry. You're never really presented a story from a Lovecraft Sorcerer's point of view in his stories, they are one of the great unknowables just like the monsters are. So in a sense even the PnP game is already outside of the realm of "a real Lovecraft experience."
Which, ya know, is ok to me. Because games based on pre-existing source material are always interpretive to some degree. And that's really to me what makes Lovecraft, Lovecraft. He focused on the soul-numbing terror people felt at meeting this stuff, that was his overarching theme. Compare and contrast 40k, a universe with the same precepts (ancient things beyond human ken, madness, the human inability to accept an alternate reality....) People lose their shit there seeing things all the time, and what they fight against is just as unbeatable, in some ways even more than Cthulhu monsters. Yet, they fight. That's a choice of the writer of the world, of course. But to me, you can't really force any player into a game where they're nothing more than a punching bag for the GM. And players can only hear "you're terrified, your world is falling apart around you...." so many times before it fails to have the desired effect and eventually hardens players to the
mechanical traps you lay.
Trust me, a bad CoC game goes like this. "GM: You see a book laying on the table." "Player 1: Not it." "Player 2: Not it." "Player 3: Not it." "Player 4: Screw that, I'm not opening it. I leave the room." And that's already the mindset of CoC players in the know when they get there. So you have to give them something to draw players other than the total sadists who just want to watch themselves blow sanity checks so they can be crazy.
So while I like the horror aspect of Lovecraft, what I actually love about his works is the setting. The Pan-dimensionality of his world, the alien cultures, corrupted bloodlines, low-tech, magic and yes, the loss of sanity. What doesn't really move me is the lack of power. That's always been a function of
who Lovecraft decided to put into the role of the main character. Compare to Arkham Horror where you're playing bad asses, magicians and mystics. CoC and Lovecraft crossbreeds are a chance for people to play a role other than "college-educated literati who has never been out of New England." Because in truth, while it makes for a good horror story, running scared does not make for a good campaign. That's not to say I endorse blasting Hastur with Tommy Guns in the final battle, that'd be ridiculous. But fighting against Byaki, Mi-Gos, Ghosts and Warlocks? I think that's a necessary part of CoC not being in this weird niche of self-abusive RPGs.
Right now I'm just sorting out and coming up with the first game and tying up and how it can lead onto other things and how everyone's characters have ended up mashed togeather
Depends on the kind of group you're running or the kind of narrative you feel you want to tell. Arkham Horror used the very simple setup that everyone has had a mythos experience (I think that's part of CoC's character creation too) and you're a party by virtue of that. Sometimes it's easier and makes for a better narrative if you let the players eventually define the nature of their group and their reason for being, than trying to orchestrate how it would be possible. Just as an alternative to a lot of story structure. (I'm struggling with that in a game I'm running right now.)
What is key in a creepy horror game is holding your cards close to your chest, so to speak.
One of the hardest things I've ever found as a GM is trying to instill fear. Just pure, realistic fear based on the thing you present. Players will fear all sorts of stuff, but they often approach it from a mechanical standpoint. (That thing ages you 30 years if it touches you! We're outnumbered 5:1. Do you know how many checks you have to make every round fighting that thing! It hits for 4D10+10 damage!)
So you really, really have to let the player's imaginations do the work for you, and like you say, that's best accomplished by giving away as little as possible for as long as the players are still intrigued and not getting annoyed. When players can't tie what they're experiencing to mechanical parts of the game, it really takes away their confidence because they have no metrics to use to assess the threat. They only have their imaginations which, again as was said, will cook up far more horrible things they might face than just about anything you planned out.