I have to ask then: have you checked out Fate of Cthulhu? It's basically Call of Cthulhu meets Terminator/Twelve Monkeys: one of the Old Ones have risen and more or less destroyed humanity, but the PCs are a last-ditch effort to be sent back in time to stop the rise before it happens. Only the knowledge of exactly what happened is imperfect, so the PCs have to figure some parts out for themselves. And the mechanism for time travel is to be sent through the metaphysical body of Yog-Sothoth which inflicts corruption on those doing so (so all future PCs have some kind of weird mutation). And of course, in true Terminator fashion, they can only send back living beings – no clothes or equipment or stuff like that. The core book presents four different scenarios, and a number of others were made as PDFs as stretch goals in the kickstarter.