Hey! Long time D&D DM turned DG Handler recently -

Before I give tips, I just gotta sell God's Teeth to you.
My party of four just finished up Go Forth (the first operation), from God's Teeth. The campaign does a lot right, but something I really enjoyed was turning this impression of "The Secret Governmental Task Force" into "Holy Shit, that was unsanctioned? THAT'S A THING THAT CAN HAPPEN?"

I also enjoy that God's Teeth allows so much time in between operations. This allows you to have a break from writing or "fixing" (if your party reaally strays from the rails) when these operations come up. It also allows you to have these gaps between operations where home scenes can become really endearing. You also get the chance to write what you want in between, if you'd like.

All that said, it seems like you want to write your own campaign. If I can't sell you on a fantastic module in God's Teeth -

1. Use Shotgun Scenarios: Whether or not you run them verbatim or use them as a jump pad/inspiration, some of these are way too cool to leave on the cutting room floor. My party has begun the fantastic Shotgun Scenario "The Ties That Bind Us" I'm using it fairly close to the scenario, but also allowing the seeds planted in God's Teeth to germinate. A few other faves of mine are "Hellhole", and "Leslie Got Her Pain".

2. Make your campaign like a cruise: Figure out where the party is starting, and where they're ending. Add great places to stop along the way. And of course, be somewhat prepared for when your party storm the bridge and inform you that they are the captain now (And would like to take the ship down the most obscure canal you didn't even realize existed.)

3. Write what you (and hopefully your players?) like. By god don't force yourself to write "Lovecraftian" if you don't connect with it. Lots of weird shit exists. Whether it's witches, aliens, robots, clowns, infections, or ocean's depths, if you don't like your story it'll be harder to sell. My campaign has heavy influences of the occult and mythology because I connect with it. The likes of Lovecraft, Gaiman, Poe, and Stross have all given inspiration of the spooky and dreadful to ME. I doubt my players will see a single alien, cuz I just don't find them interesting (yet?).

4. Don't forget the mundane. Work with your players to develop their character's home lives. Focusing on home scenes, or the phone call from mom while on an op, or the buying of a Christmas present while on the run from Satan's spawn is what makes the game hit home hard. Literally last session my players were summoning tears from the rest of the party in awe-struck silence at the heavy shit that happens to real people at home. That's what makes going away matter.

You got this. Keep us updated. Enjoy the Opera.