So, it has already been suggested, but I will detail here why I think World of Darkness does suit your needs. I'm not saying it suits them more than the other systems evoked, for lack of having actually played most, if any, of them. But here's how, according to my experience with them, White Wolf's system and setting fit the bill.
1. The Conspiracy theme is all over the place.
While each specific splatbook has its own theme, it's a basic assumption of the World of Darkness as a whole : the world is not as it seems, the supernatural creeps beneath the surface, in every shadow. This is even more real when playing "Mortals" (characters with no supernatural template) and Hunters, but even supernaturals have schemes and hidden truths of their own (the most egregious example being the Ascension War of the Archmages).
2. A game of Horror and Mystery
The system is geared towards "low" powered characters. It will take alot of effort and experience (and a few good twists of fate) to end up with a world shaker. This is because the game is intended for the telling of horror and mystery stories at its heart. Even Vampires can be confronted with old legends (who end up being the true story of an Ancient), dig up knowledge that was not meant for man or face abominations from another realm of existence (which may or may not be that hard to reach). The Morality system ensures that a character that behaves like a madman does so because he is actually descending into madness.
3. "Experience with Firearms, capacity for teamwork a plus"
Obviously, not every character can know all skills, but there is also no skill to end all skills. No "I win" discipline/arcana/transmutation/whatever. No Auspice to give you easy access to every Gift. This ensures that characters may have a broad skill set, but must specialize to be effective, and thus cooperate in the face of varying obstacles.
4. May translate well to the past
This part is a bit shaky as I can't really back it up, but the skill set should still hold water in the past, at least up to 1860, where Drive could apply to carriages and Firearms to those unwieldy pistols of old (Computer is probably a bit of a stretch, though). Still, the themes are timeless and, even in the core books, many of the organizations and events described reach into the past, and there are even some recent books that touch on specific periods of the past (Victorian Lost, Mage Noir...) that can help in getting a better picture.
A few points of contention
There are, of course, points that are not addressed, that may require work on the Storyteller's or the Players' part.
- While the Contacts/Allies are not as detailed as desired, the system offers a number of Social Merits (namely Contacts, Mentor, Allies, Status to remain in the Core book context) that, while abstract, are to be used in this way.
- A clue trail mechanism -similar to what can be found in Gumshoe- is apparently absent, though it could be ignorance on my part. Quite a few books in the collection have offered alternate systems and interpretations of rules so that may be in one I haven't read. But I wouldn't bet on that, and I don't see an easy way to houserule it into the framework of this particular system.
You would need a fair number of books. It's probably going to work best with a full-mortal or Hunter party, but properly rendering the various monsters of the week will require the storyteller to have their splatbooks at hand. But I've successfully GMed a short series of Mage episodes that had more of a lighter mood but still fit the mold of the mystery-with-conspiracy-background series we love.